Toward a Three-Dimensional Crustal Structure of the
Dead Sea region from Local Earthquake Tomography
Thesis submitted to the Senate of Tel-Aviv University
for the degree of Doctor of Philosophy
by
Freddy Aldersons
Under the supervision of
Prof. Zvi Ben-Avraham (TAU)
and Prof. Eduard Kissling (ETH)
June 2004
To Marilena
ii
Contents
v
Abstract
Chapter 1
Introduction
Chapter 2
Lower-crustal strength under the Dead Sea basin from local
earthquake data and rheological modeling
2.1 Introduction
2.2 Geological setting
2.3 Seismicity
2.4 Rheology
2.5 Discussion and conclusions
Acknowledgments
4
4
6
7
15
19
21
Methods of a new picking system: MannekenPix
3.1 Automatic picking
3.2 MannekenPix
3.3 The four steps of MannekenPix
3.3.1 Wiener filter
Linear least-squares optimal filtering of stationary time series
Stochastic and data-adaptive Wiener filters
Power spectrum estimation
Classical methods of power spectrum estimation
The Maximum Entropy Method (MEM)
Burg’s algorithm
Selection of the model order in MEM
Properties of an MEM spectrum
Power spectrum estimation in MannekenPix
Application of the Wiener filter
Wiener filter and deconvolution applied to a synthetic example
3.3.2 Automatic picking
3.3.3 Delay corrections
3.3.4 Weighting
Discriminant analysis
The discriminating variables of MannekenPix
22
23
25
27
28
28
31
33
34
38
40
42
43
47
48
49
54
56
61
62
63
Chapter 3
1
iii
Chapter 4
High-quality automatic picking of local earthquake data
from the Dead Sea region
4.1 Methodology
4.2 Data set characterization
4.3 Picking rate and accuracy
4.4 Picking uncertainty
4.5 A simple relocation
67
68
71
76
82
89
Conclusions
Lower-crustal strength under the Dead Sea basin
A new picking system: MannekenPix
Deconvolution
91
91
92
93
Application of MannekenPix to the Dead Sea region
Application of MannekenPix to the seismicity of Italy
94
95
Appendix A
Abbreviations
97
Appendix B
Source function parameters and seismograph response of the
Wiener-filtered synthetic example (Figure 3.6)
99
Chapter 5
Appendix C
GII and JSO Station Coordinates
107
References
110
Acknowledgments
122
iv
Abstract
We studied the local seismicity of the Dead Sea basin for the period 1984-1997. Sixty percent of
well-constrained microearthquakes (ML ≤ 3.2) nucleated at depths of 20-32 km and more than 40
percent occurred below the depth of peak seismicity situated at 20 km. With the Moho at 32 km,
the upper mantle appeared to be aseismic during the 14-year data period. A relocation procedure
involving the simultaneous use of three regional velocity models reveals that the distribution of
focal depths in the Dead Sea basin is stable. The lower-crustal seismicity under the basin is not
an artifact created by strong lateral velocity variations or data-related problems. An upper bound
depth uncertainty of ± 5 km is estimated below 20 km, but for most earthquakes depth
mislocations should not exceed ± 2 km. A lithospheric strength profile has been calculated.
Based on a surface heat flow of 40 mWm-2 and a quartz-depleted lower crust, a narrow brittle to
ductile transition might occur in the crust around 380°C at a depth of 31 km. For the upper
mantle, the brittle to ductile transition occurs in the model at 490ºC and at 44 km depth. The
absence of micro-seismicity in the upper mantle remains difficult to explain.
Within the framework of local earthquake tomography, a new automatic picking system called
MannekenPix has been developed in order to collect a high-quality set of picking data from the
Dead Sea region. In another work, this data set would then become the input of a high-resolution
travel-time tomographic study of the crustal structure of the basin. In the first step of
MannekenPix, the seismograms are filtered by a high-fidelity Wiener filter in order to increase
the signal-to-noise ratio of the P-wavetrain before picking. The Wiener filter of MannekenPix
uses the maximum entropy method to estimate power spectral densities, a method particularly
well adapted to short data segments. The picking is performed in the second step by the robust
and versatile Baer-Kradolfer (Baer and Kradolfer, 1987) picking engine. If a valid pick has been
found, a variable delay correction is then applied in the third step in order to reduce the inherent
delay of the Baer-Kradolfer algorithm arrivals. In the fourth step, the weighting engine provides
a statistical estimate of the uncertainty. For each data set, the weighting engine has to be
calibrated first by a multiple discriminant analysis performed on user-supplied reference picks
and weights.
By using MannekenPix to pick the seismograms from well-constrained earthquakes of the Dead
Sea region, 526 (99.1 %) out of 531 earthquakes are locatable by automatic picking. Out of
15,250 seismograms, 6,889 (45.2 %) were routinely picked and 7,089 (46.5 %) were
v
automatically picked. On the calibration data set, the average discrepancy between the routine
picking and the reference picking is –0.037 sec, with a standard deviation of 0.121 sec. The
average discrepancy of the automatic picking is +0.007 sec with a standard deviation of only
0.066 sec. For the complete data set, 3,058 phases (43.1 %) of the 7,089 automatic P picks fall
into predicted weight 1 (absolute uncertainty not greater than 40 msec), 1,173 (16.5 %) fall into
class 2 (absolute uncertainty between 40 msec and 80 msec), 1,554 (21.9 %) fall into class 3
(absolute uncertainty between 80 msec and 140 msec) and 1,304 (18.4 %) fall into class 4
(absolute uncertainty greater than 140 msec). The results from a totally out-of-sample set of
reference picks and weights confirm the stability of predicted weights on unseen data.
Di Stefano et al. (2004, to be submitted) present the application of MannekenPix to about
240,000 seismograms from nearly 29,000 local earthquakes routinely recorded by the Italian
national seismic network during the period 1998-2001. MannekenPix was able to produce
103,131 P picks (73% of the 139,500 routine onsets) from 23,108 events out of 28,900 events.
About 17,130 phases (17 %) of the 103,131 fall into class 1 (absolute uncertainty not greater than
0.1 sec) and 15,429 (15 %) fall into class 2 (absolute uncertainty between 0.1 sec and 0.2 sec).
Results show that MannekenPix arrival times for classes 1 and 2 combined, produce a
distribution of residual times with a much smaller standard deviation than for the CSI bulletin.
This means that a significant increase in the quality of the data set has been gained, coming at the
price of a reduced quantity. The application of MannekenPix to the very large and
inhomogeneous dataset of waveforms recorded in Italy from 1998 to 2001 yields nearly 33,000
high-quality weighted picks and polarities. By using MannekenPix we achieved our goal to build
a new dataset of P-wave arrival times and polarities belonging to user-defined classes 1 and 2
(the highest qualities) with associated error estimations. The analysis of relocation residuals and
the time versus distance plots for these classes show the effectiveness of the picking system.
Although the hit rate of MannekenPix 1.6.2 applied to this large and noisy dataset did not exceed
75 % of the rate of an expert seismologist, the consistency of computed arrivals and polarities
and their rapid estimation are very suitable to substitute bulletin data, solving the typical problem
of extending consistency and quality to large datasets, and saving a great amount of time. We
believe that the improved seismic dataset is suitable to refine the seismic tomography and to
improve the knowledge of the local and regional stress fields in the Italian peninsula through the
determination of a large number of focal mechanisms for well-located events, extending the
analysis to small magnitudes and past events.
vi
Chapter 1
Introduction
The Dead Sea Transform (Figure 1.1a) is an intracontinental plate boundary resulting from the
late-Cenozoic breakup of the Arabo-African continent. This boundary extends over 1,000 km
from the zone of sea floor spreading at the southern tip of the Sinai Peninsula to the TaurusZagros zone of convergence in Turkey (Freund, 1965). The Dead Sea basin (Figure 1.1b) is an
active pull-apart (Quennell, 1958) located along the Dead Sea Transform. The amount of leftlateral motion along the Transform in the Dead Sea region is estimated at 105 km (Quennell,
1958; Freund et al., 1970). Motion along the Transform started around 20 Ma ago during
Miocene times (Bartov et al., 1980). Although the Dead Sea basin originated at the beginning of
the Transform motion, it did not develop into a topographic low before early Pliocene
(Garfunkel, 1997). Pliocene sediments are mostly composed of evaporites, among which halite is
the main constituent. Deformation of Pliocene salt has created numerous diapirs in the basin
(Neev and Hall, 1979). During Pleistocene times, the basin subsidence accelerated (ten Brink and
Ben-Avraham, 1989) and allowed the accumulation of several kilometers of lacustrine clastics,
carbonates and evaporites. Today the basin is a morphotectonic depression over 130 km long and
7-18 km wide. It is a seismically active section (van Eck and Hofstetter, 1989, 1990) along the
Dead Sea Transform, for which some 4,000 years of combined archaeological, historical and
instrumental seismicities are documented (Ben-Menahem, 1991). Recent articles on the tectonics
of the Dead Sea basin can be found in Cloetingh and Ben-Avraham (2002).
The Dead Sea basin and its surroundings have been monitored locally during nearly 20 years by
permanent digital seismic stations. In addition, the region has been the focus of detailed
geophysical studies during past decades. These studies include bathymetry (Neev and Hall,
1979), seismic reflection (Neev and Hall, 1979; ten Brink and Ben-Avraham, 1989), seismic
1
Figure 1.1 Regional setting of the Dead Sea basin. (a) The East-Mediterranean region. (b) The Dead Sea region.
Five hundred thirty-one well-locatable earthquakes (1984-2001) in the vicinity of the Dead Sea basin, recorded by
short-period stations (triangles) of GII (Israel) and JSO (Jordan). The square grid fill defines the Dead Sea basin.
DST: Dead Sea Transform. Topographic shaded relief derived from Globe 1-km elevation data.
refraction (Ginzburg et al., 1981; Ginzburg and Ben-Avraham, 1997), wide-angle reflectionrefraction (DESERT Group, 2004), gravity (ten Brink et al., 1990; ten Brink et al., 1993),
magnetism (Frieslander and Ben-Avraham, 1989; Al-Zoubi and Ben-Avraham, 2002), heat flow
(Ben-Avraham et al., 1978) and seismicity (van Eck and Hofstetter, 1989, 1990).
Local earthquake travel-time tomography can provide information in a depth range that cannot
be imaged by seismic reflection methods, and it can resolve details of the crustal structure that
are not accessible to regional studies. It could be a particularly helpful technique to image the
lower crust under the Dead Sea basin, for which little is known and whose role in the
development of the basin is poorly understood. Two local earthquake tomographic studies
(Rabinowitz et al., 1996; Rabinowitz and Mart, 2000) have already been performed in the Dead
Sea basin but with very small data sets.
2
The main purpose of this work is to collect a high-quality set of picking data from the Dead Sea
region through the development of an automatic picking system. In another work, this data set
would then become the input of a high-resolution travel-time tomographic study of the crustal
structure of the basin and vicinity.
Routine earthquake locations in the Dead Sea region suggest that an anomalously high number of
micro-earthquakes might have nucleated in the lower-crust under the basin. We studied the local
seismicity of the Dead Sea basin for the period 1984-1997. This seismological study,
complemented by a rheological strength profile of the lithosphere, is presented in Chapter 2.
The methods underlying the new picking system called MannekenPix are described in Chapter 3.
Built around the Baer-Kradolfer (1987) single-trace picking algorithm, MannekenPix first
reduces the noise on the seismograms by applying an adaptive high-fidelity Wiener filter where
power spectral densities are estimated from short data segments. The Wiener filter of
MannekenPix uses the maximum entropy method (MEM) which is particularly well adapted to
short data segments. The Baer-Kradolfer (1987) picking algorithm is described next and the
delay it introduces is corrected by two adaptive corrections. Finally, MannekenPix provides a
statistical estimate of the uncertainty affecting the automatic picks following a calibration
derived from reference picks and weights provided by the user.
Chapter 4 presents the case study of the application of MannekenPix to the local data set
gathered for the Dead Sea region. In order to allow potential users of MannekenPix to better
evaluate the profile of the data, a detailed characterization of the data set is presented. The
picking hit rate and accuracy are examined next, followed by the estimated picking uncertainties.
Residual times from a simple relocation conclude Chapter 4.
The conclusions of the work are presented in Chapter 5, along with the main results from the
application of MannekenPix to the seismicity of Italy.
3
Chapter 2
Lower-crustal strength under the Dead Sea basin from local
earthquake data and rheological modeling
F. Aldersons, Z. Ben-Avraham, A. Hofstetter, E. Kissling and T. Al-Yazjeen
Earth and Planetary Science Letters (2003) 214 129-142
ABSTRACT
We studied the local seismicity of the Dead Sea basin for the period 1984-1997. Sixty percent of
well-constrained microearthquakes (ML ≤ 3.2) nucleated at depths of 20-32 km and more than 40
percent occurred below the depth of peak seismicity situated at 20 km. With the Moho at 32 km,
the upper mantle appeared to be aseismic during the 14-year data period. A relocation procedure
involving the simultaneous use of three regional velocity models reveals that the distribution of
focal depths in the Dead Sea basin is stable. Lower-crustal seismicity is not an artifact created by
strong lateral velocity variations or data-related problems. An upper bound depth uncertainty of
± 5 km is estimated below 20 km, but for most earthquakes depth mislocations should not exceed
± 2 km. A lithospheric strength profile has been calculated. Based on a surface heat flow of 40
mWm-2 and a quartz-depleted lower crust, a narrow brittle to ductile transition might occur in
the crust around 380°C at a depth of 31 km. For the upper mantle, the brittle to ductile transition
occurs in the model at 490ºC and at 44 km depth. The absence of micro-seismicity in the upper
mantle remains difficult to explain.
2.1 INTRODUCTION
It is commonly assumed (Meissner and Strehlau, 1982; Chen and Molnar, 1983) that no
significant seismicity exists in rifts at depths greater than 15-20 km. The lower crust in
continental extension zones is indeed often aseismic due to elevated temperatures accompanying
lithospheric thinning. In relation to a more recent trend of research (Cloetingh and Burov, 1996;
Maggi et al., 2000; Jackson, 2002), microearthquakes from Israel and Jordan suggest that the
4
Figure 2.1 The Dead Sea region. Topographic shaded relief derived from Globe 1-km elevation data. The square
grid fill defines the Dead Sea basin. Seismicity: 410 well-constrained earthquakes (1984-1997) recorded by shortperiod stations (triangles) of GII (Israel) and JSO (Jordan). DST: Dead Sea Transform.
lower crust (20-32 km) has probably kept a significant strength under the Dead Sea basin. A
similar behavior of the lower crust in continental extension regimes has already been observed,
mainly in the western branch of the East African rift system (Shudofsky et al., 1987; Nyblade
and Langston, 1995; Camelbeek and Iranga, 1996) and in the Baikal rift system (Déverchère et
al., 2001). Anomalously deep crustal earthquakes are also known to occur in the western United
States (Wong and Chapman, 1990; Bryant and Jones, 1992) and below the northern Alpine
foreland of Switzerland (Deichmann and Rybach, 1989). Focal depths of earthquakes are
generally difficult to constrain tightly. The most reliable estimates are usually those derived from
local earthquake data if well-distributed stations are present and a good knowledge of the
velocity field has been gained. The Dead Sea basin and its surroundings (Figure 2.1) have been
monitored locally for more than 10 years by permanent digital seismic stations. In addition, the
5
region has been the focus of detailed geophysical studies during past decades. These studies
include bathymetry (Neev and Hall, 1979), seismic reflection (Neev and Hall, 1979; ten Brink
and Ben-Avraham, 1989), seismic refraction (Ginzburg et al., 1981; Ginzburg and BenAvraham, 1997), gravity (ten Brink et al., 1990; ten Brink et al., 1993), magnetism (Frieslander
and Ben-Avraham, 1989; Al-Zoubi and Ben-Avraham, 2002), heat flow (Ben-Avraham et al.,
1978) and seismicity (van Eck and Hofstetter, 1989, 1990).
Constraints provided by these studies not only lead to more robust results, they also allow the
development of geophysical models better tuned to the geological environment. In this article we
present evidence from local earthquake data and rheological modeling that lead us to
acknowledge the existence of a significant lower-crustal strength under the Dead Sea basin.
2.2 GEOLOGICAL SETTING
The Dead Sea Transform (Figure 2.1) is an intracontinental plate boundary resulting from the
late-Cenozoic breakup of the Arabo-African continent. This boundary extends over 1,000 km
from the zone of sea floor spreading at the southern tip of the Sinai Peninsula to the TaurusZagros zone of convergence in Turkey (Freund, 1965). The Dead Sea basin is an active pullapart (Quennell, 1958) located along the Dead Sea Transform. The amount of left-lateral motion
along the Transform in the Dead Sea region is estimated at 105 km (Quennell, 1958; Freund et
al., 1970). Motion along the Transform started around 20 Ma ago during Miocene times (Bartov
et al., 1980). Although the Dead Sea basin originated at the beginning of the Transform motion,
it did not develop into a topographic low before early Pliocene (Garfunkel, 1997). Pliocene
sediments are mostly composed of evaporites, among which halite is the main constituent.
Deformation of Pliocene salt has created numerous diapirs in the basin (Neev and Hall, 1979).
During Pleistocene times, basin subsidence accelerated (ten Brink and Ben-Avraham, 1989) and
allowed the accumulation of several kilometers of lacustrine clastics, carbonates and evaporites.
Today the basin is a morphotectonic depression over 130 km long and 7-18 km wide (Figure
2.1). It is a seismically active section (van Eck and Hofstetter, 1989, 1990) along the Dead Sea
Transform, for which some 4,000 years of combined archaeological, historical and instrumental
seismicities are documented (Ben-Menahem, 1991). For the northern half of the Dead Sea basin
(main lake and salt pans), earthquakes of ML ≥ 5.8 ± 0.2 have a recurrence interval of
approximately 160 years (Shapira, 1997). The last earthquake of such a magnitude (estimated
magnitude 6.2 by Turcotte and Arieh, 1988) occured in the main lake (Shapira et al., 1993) in
1927 at an unknown depth.
6
2.3 SEISMICITY
Figure 2.2 displays a depth section of seismicity along the Dead Sea Transform between AqabaElat in the south and the Sea of Galilee in the north for the period 1984-1997. Out of 2,283
routinely recorded events, a first selection resulted in 653 events with at least 8 P readings each
and an azimuthal gap smaller than 180 degrees. To further exclude events with poorly
constrained depths, an empirical criterion based on the epicentral distance to the nearest station
(Dmin) was adopted for events with an estimated depth of less than 21 km (Figure 2.3). For
depths greater than 21 km, all events from the first selection appeared as valid candidates and
were included. Two hundred forty-three events from the first selection of 653 events were
rejected while the remaining were included and are the 410 earthquakes displayed in Figure 2.1
and Figure 2.2. Our study focuses on the Dead Sea basin and discusses whether the apparently
unusual focal depths observed there are part of a broader phenomenon or represent a local
anomaly.
We started the Dead Sea seismicity study by a series of relocations aimed at detecting flaws like
unstable local minima solutions. Most first P arrivals from earthquakes nucleating in the basin
were carefully repicked manually, and weighted according to the quality of their onsets. Fortytwo well-constrained earthquakes qualified (Figure 2.4a) and relocations were performed with
program Velest (Kissling, 1994).
Figure 2.2 Depth section of well-constrained seismicity (410 earthquakes, 1984-1997) along the Dead Sea
Transform (DST) from Aqaba-Elat to the Sea of Galilee. The square grid fill defines the Dead Sea basin on the map.
Conrad and Moho discontinuities from Ginzburg et al. (1981).
7
Depth Z (km)
0
5
10
15
20
25
30
60
60
2
D(Z) = -0.05 * Z + 2.5 * Z
Rejected Events (243): Dmin > D
Selected Events (410): Dmin < D
55
50
50
45
45
40
40
35
35
30
30
25
25
20
20
15
15
10
10
5
5
0
Dmin (km)
Dmin (km)
55
0
0
5
10
15
20
25
30
Depth Z (km)
Figure 2.3 Near-epicentral distance selection for 653 events from Aqaba-Elat to the Sea of Galilee (P ≥ 8 and Gap
< 180º). Z is the estimated hypocentral depth and Dmin is the epicentral distance to the nearest station.
X (km)
Vp (km/s)
160 170 180 190 200 210 220 230
130
N
(a)
4
5
7
110
100
100
Israel
70
Y (km)
80
Oceana
20
20
Lower Crust
30
Mantle
Dead Sea
L1
L2
Upper Crust
10
L4
20
20
Lower Crust
Dead
Sea
30
50
10 < Z < 20
20 < Z < 25
25 < Z < 32
GII
40
30
Jordan
10
Upper Crust
20
(d)
10
30
Mantle
20
160 170 180 190 200 210 220 230
0
20
Lower Crust
30
JSO
20
30
L6
Mantle
0
Depth (km)
50
60
L5
(c)
Depth (km)
Depth Z (km)
0 < Z < 10
0
10
L3
30
60
(b)
Depth (km)
80
Depth (km)
90
0
10
Upper Crust
30
Jordan
Israel
10
0
90
8
Depth (km)
110
40
6
0
Depth (km)
120
Y (km)
3
130
120
70
2
2
3
4
5
6
7
8
Vp (km/s)
X (km)
Figure 2.4 (a) Structural units and stations (triangles) in the Simulps relocation. Epicenters and depths of the set of
42 earthquakes (squares) relocated with Velest. (X,Y) are Rectangular Israel Grid coordinates (Survey of Israel).
Oceana is a salt quarry. (b,c,d) The three velocity models used in the Simulps relocation.
8
Model Israel (Figure 2.4b) was applied to the whole volume of earthquakes and stations. This
model is similar to the routine model used by the Geophysical Institute of Israel (GII) but we
derived it from quarry blasts located in the vicinity of the Dead Sea basin. Several relocations
were conducted with Velest during which the effects of various initial conditions were explored.
During these relocations, it was not considered a significant problem if the focal depths of a few
earthquakes shifted up or down. Our main criterion was the stability of the distribution itself, not
the perfect stability of every estimate. Tests like these are usually good at detecting flaws in
hypocentral parameters like local minima solutions. No such flaws were ever observed. Depths
derived from model Israel are stable. The distribution of depths in the Dead Sea basin is plotted
in Figure 2.5a. It shows that 60 percent of well-constrained microearthquakes (ML ≤ 3.2)
nucleated at depths of 20-32 km and that more than 40 percent occurred below the depth of peak
seismicity situated at 20 km. The upper mantle appeared to be aseismic during the 14-year data
period.
Relative Frequency (%)
0
5
10
15
Relative Frequency (%)
0
5
10
15
0
0
(a)
(b)
5
5
Upper Crust
10
Upper Crust
Upper Crust
10
15
20
20
25
Lower Crust
Lower Crust
Lower Crust
30
Depth (km)
Depth (km)
15
25
30
0
5
10
15
0
Relative Frequency (%)
5
10
15
Relative Frequency (%)
Cross-Correlation
-1.0
-0.5
0.0
0.5
1.0
-5
-4
-3
-2
-1
0
1
2
3
4
5
-1.0
-0.5
0.0
0.5
Lag (km)
Lag (km)
-5
-4
-3
-2
-1
0
1
2
3
4
5
(c)
1.0
Cross-Correlation
Figure 2.5 Focal depths of well-constrained earthquakes in the Dead Sea basin. (a) Depth distribution of 42
earthquakes located with regional velocity model Israel (Figure 2.4b) in Velest. (b) Depth distribution of 32
earthquakes located with three regional velocity models in Simulps (Figure 2.4). (c) Cross-correlation of (a) and (b)
between 17 and 32 km depth. The dashed lines delineate the 95 % confidence interval assuming (a) and (b) to be
uncorrelated. A significant correlation of 0.66 is found at Lag = + 2 km.
9
Although depths derived from model Israel are stable, velocities in the uppermost 9 km of the
model are too high for the Dead Sea basin (compare model Israel versus model Dead Sea, Figure
2.4b and Figure 2.4c). This might create an artificial deepening of focal depths for earthquakes
nucleating in the basin. In order to evaluate this possibility, program Simulps (Thurber, 1984)
was also used to relocate earthquakes.
In each of the three structural units of Figure 2.4a, a one-dimensional velocity model was
defined. The boundaries between the three units were derived from the maximum gradient of
gravity (ten Brink et al., 1993). All three models are rather similar below the depth of 10 km.
Models Israel and Jordan (El-Isa, 1990; JSO, 1993) are rather similar throughout. The first layer
is however thinner in model Jordan compared to model Israel and no contrast between the upper
and lower crust is present in model Israel. The upper crust in the Dead Sea velocity model was
derived from a refraction profile in the north basin of the Dead Sea (Ginzburg and Ben-Avraham,
1997), while the lower crust was derived from a deep refraction experiment by Ginzburg et al.
(1981). From the abrupt termination of the cusp (Bullen, 1960; Ginzburg et al., 1979), the
authors infer the existence of a 5-km transition zone between the main lower-crustal velocity of
6.6 km/s and the upper mantle velocity of 7.9 km/s, a feature apparently missing in adjacent
areas outside the rift. According to the same study, the Dead Sea basin is underlain by a Moho at
about 32 km depth, a value supported by gravity modeling (ten Brink et al., 1993).
Earthquakes were relocated by Simulps according to the velocities and boundaries of the three
structural units. No attempt was made to derive optimal velocities from the data themselves. The
selection of a fine discretization grid resulted in restrictions on the maximum size of the model.
Due to the smaller number of stations available, only 6 P arrivals were required for qualifying
events. Among the 42 earthquakes relocated by Velest, 32 qualified for the Simulps relocation.
Epicentral distances to stations never exceeded 85 kilometers and no more than 11 arrivals per
earthquake could be observed. Most seismic rays were confined to the upper crust and rays from
deeper earthquakes quickly turned up. Figure 2.5b displays the depth distribution using Simulps.
The lower-crustal seismicity remains in place and the whole distribution displays features similar
to those in the distribution computed with Velest, although deeper by 2 km in the lower half.
Nearly identical results were obtained without the transition zone at the base of the lower crust.
One should not however conclude that the Simulps relocation is more reliable than the Velest
relocation. The purpose of the Simulps relocation was to test the possible influence of slow
velocities in the upper section of the Dead Sea basin. The results show that the lower-crustal
seismicity detected by Velest is not an artifact created by these slow basinal velocities.
10
Two independent evaluations of the uncertainty on depths derived from model Israel have been
made. First, we applied perturbations to model Israel and relocated the 42 well-constrained
earthquakes with resulting models in Velest. This method evaluates the sensitivity of depths to
departures from model Israel, and it provides individual error bars for each of the 42
earthquakes. Velocity perturbations of ± 5 %, ± 10 %, and depth perturbations of ± 10 %, ± 20
%, were added to model Israel (Table 2.1 and Figure 2.6a). Velocity perturbations of +10 % for
layer 2 and -10 % for layer 3 were not applied because they would have created some unrealistic
velocity inversions with depth from layer 2 to layer 3. Consequently and in order to preserve
symmetry around model Israel, velocity perturbations of -10 % for layer 2 and +10 % for layer 3
were also not applied. The bottom depth of layer 3 (the Moho) was not perturbed by more than ±
9 % following gravity results implying that the Moho should not be anomalously elevated by
more than 2-3 km under the Dead Sea basin (ten Brink et al., 1990; ten Brink et al., 1993).
Perturbations of ± 0.250 km/s around the upper mantle velocity of 7.9 km/s appeared also to be
quite sufficient. All combinations of perturbations defined in Table 2.1 represent a set of 16,875
velocity models.
Depths and error bars derived from this set are plotted in Figure 2.6b. Two main conclusions
emerge. First, according to the 5th to 95th percentile intervals, at least 25 % of well-constrained
microearthquakes under the Dead Sea basin can belong neither to the upper-crustal seismicity
nor to a hypothetical upper-mantle seismicity. Second, error bars tend to narrow for deeper
earthquakes (Figure 2.7), expressing a lesser sensitivity to model perturbations in the lower crust
compared to the upper crust.
Table 2.1 Perturbations to model Israel
Layer
VP (km/s)
VP perturbation (%)
Layer bottom (km)
Bottom perturbation (%)
Layer 1
3.150
3.325
3.500
3.675
3.850
-10.0 %
-5.0 %
0.0 %
+5.0 %
+10.0 %
Layer 2
5.225
5.500
5.775
-5.0 %
0.0 %
+5.0 %
Layer 3
5.985
6.300
6.615
-5.0 %
0.0 %
+5.0 %
3.280
3.690
4.100
4.510
4.920
8.640
9.720
10.800
11.880
12.960
29.000
30.450
31.900
33.350
34.800
-20.0 %
-10.0 %
0.0 %
+10.0 %
+20.0 %
-20.0 %
-10.0 %
0.0 %
+10.0 %
+20.0 %
-9.1 %
-4.5 %
0.0 %
+4.5 %
+9.1 %
Layer 4
7.650
7.900
8.150
-3.2 %
0.0 %
+3.2 %
Half-space
11
Vp (km/sec)
3.0
3.5
4.0
0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
0
Model "Israel"
L1
(a)
5
5
L2
10
15
15
20
20
L3
25
25
30
30
L4
35
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
Depth (km)
Depth (km)
10
35
8.5
Vp (km/sec)
Percentiles
5
0
10
5
Upper Crust
0
(b)
5
25
10
10
Mean
15
15
75
90
95
20
20
25
Depth (km)
Depth (km)
50
25
Lower Crust
30
30
Upper Mantle
35
35
Figure 2.6 (a) Depth and velocity perturbations defining 16,875 models around model Israel. L1 to L4 are the four
layers of model Israel. (b) Hypocentral depths and error bars for the 42 earthquakes relocated by Velest with
perturbed models defined in (a). Earthquakes sorted according to increasing median (50th percentile) depth. The
black dashed line marks depths obtained with model Israel.
Median depth (km)
5
10
15
20
25
30
13
12
5th percentile
11
95 percentile
th
12
11
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
0
Distance to median depth (km)
Distance to median depth (km)
13
0
5
10
15
20
25
30
Median depth (km)
Figure 2.7 Upper-bound to the uncertainty on depths (dashed line) from perturbations to model Israel.
12
This is a coherent behavior of a distribution of depths since seismic rays from shallower
earthquakes tend to propagate twice (by refraction) through more layers than deeper earthquakes
do. Error bars show also that several lower-crustal earthquakes close to 20 km depth could have
nucleated in the upper crust but the reverse is also true, a similar number of upper-crustal
earthquakes could have nucleated in the lower crust. The net result is then very close to the
original distribution of depths. Close to the Moho, only the two deepest earthquakes are realistic
candidates for an upper-mantle origin but model Israel locates them in the lower crust. From
Figure 2.7, an upper-bound to the uncertainty in the range of depths 21-32 km is then ± 5 km.
As a second approach to depth uncertainties, we determined true depth errors for a series of
blasts from quarry Oceana. Oceana is a Dead Sea salt quarry located on the western salt pan
south of the main lake and only 15 km away from the main cluster of deepest earthquakes
(Figure 2.4a). We only considered well-constrained blasts with at least 8 P readings, and an
azimuthal gap not greater than 150 degrees. In addition, we required Dmin (distance of closest
station to the estimated epicenter) to be 3-4 km and we rejected events not explicitly attributed to
Oceana by the GII analysts. Figure 2.8 shows that the number of P readings for the 24 Oceana
blasts is lower than for the 42 earthquakes while gaps are similar. It shows also that earthquakes
below 20 km depth have all a Dmin value lower than the estimated depth, an important feature
regarding depth control. As a whole, Oceana blast data are then not as well-constrained as our set
of earthquakes.
Nevertheless, Figure 2.9b reveals that Oceana blasts located with model Israel do not display true
depth errors greater than 2 km, with the exception of two outliers. Since blast locations are
generally less accurate than earthquake locations in a given area due to poorly approximated
refracted rays near sources at the surface (Kissling, 1988), even smaller depth mislocations are
possible for earthquakes in the basin.
13
Depth (km)
1
2
3
4
5
35
35
30
30
30
25
25
25
20
20
20
15
15
15
10
10
10
5
5
5
0
0
Gap (deg)
0
35
0
5
10 15 20 25 30 35
0
1
2
3
4
5
180
180
150
150
150
120
120
120
90
90
90
60
60
60
30
30
30
0
0
5
10 15 20 25 30 35
0
-1
0
1
2
3
4
5
35
35
35
30
30
30
25
25
25
20
20
20
15
15
15
10
10
10
5
5
5
0
0
0
5
10 15 20 25 30 35
Depth (km)
Figure 2.8 (Left) Number of P phases, azimuthal
gap and Dmin for the 42 earthquakes located with
model Israel in Velest. (Right) Same as (Left) but
for 24 blasts of quarry Oceana. Dmin is the
distance of the closest station to the estimated
epicenter. The dashed line outlines values for
which Dmin is equal to the estimated depth.
0
-1
180
0
Dmin (km)
-1
P Phases
10 15 20 25 30 35
Gap (deg)
5
Dmin (km)
P Phases
0
Depth (km)
0
-1
0
1
2
3
4
5
X (km)
Depth (km)
185
190
195
200
75
75
(a)
LISJ
70
70
Oceana
65
60
60
55
55
SDOM
185
190
195
200
X (km)
(b)
0
0
1
1
2
2
3
3
4
4
5
5
Depth under Dead Sea Level (km)
14
Depth under Dead Sea Level (km)
Figure 2.9 (a) Epicentral locations (model Israel in Velest) of 24
Oceana quarry blasts. X and Y are Cassini-Soldner (Survey of Israel)
projection coordinates. Epicenters as white circles. (b) Depth error of
blasts plotted in (a).
Y (km)
Y (km)
DSD2
65
2.4 RHEOLOGY
A lithospheric strength profile (e.g. Ranalli, 1987) has been calculated using the five crustal
layers defined in velocity model Dead Sea (Figure 2.4c) and one additional layer for the upper
mantle. Below 20 km, the lower crust was modeled as diabase, a lithology consistent with the
main value of 6.6 km/s (Christensen and Mooney, 1995) in layer 5 of the velocity model. The
transition zone at the base of the crust was discarded.
We derived the geotherm for the Dead Sea basin from the one-dimensional equilibrium heat
conduction (Turcotte and Schubert, 2002) equation
∂ 2T
A
=−
2
∂z
k
(2.1)
where T is the temperature, z the depth, A the radiogenic heat generation rate per unit volume,
and k the thermal conductivity. This second-order differential equation can be solved given two
boundary conditions. Assuming the surface to be at z = 0 and z increasing with depth, the surface
heat flow and surface temperature as boundary conditions are respectively Q = − k ∂T / ∂z = −Q0
at z = 0, and T = T0 at z = 0. The surface heat flow Q = −Q0 is negative because heat is flowing
upwards and z is positive downwards. For a layered model where each layer i has a given
thermal conductivity ki and a radiogenic heat generation rate Ai, we obtain the temperature Tn,z in
layer n at a depth z from the surface:
Tn , z = −
n −1
⎛ A
An 2 ⎡ n −1 ⎛ Ai +1 Ai ⎞
Q ⎤
A ⎞
z + ⎢∑ ⎜
− ⎟ zi + 0 ⎥ z + ∑ ⎜ i − i +1 ⎟ zi2 + T0
k1 ⎦
2k n
2ki +1 ⎠
i =1 ⎝ 2ki
⎣ i =1 ⎝ ki +1 ki ⎠
(2.2)
where zi is the bottom depth of layer i. Using six layers and average parameters, the onedimensional geotherm is only sensitive to two variables: the surface heat flow, and the thermal
conductivity in the first layer. These two variables exert a great influence on the slope of the
geotherm at the surface and therefore play a major role on the estimated temperature in the
deeper part of the model. The average measured heat flow in the northern Dead Sea basin is 38
mWm-2 (Ben-Avraham et al., 1978; Ben-Avraham, 1997) and it is 42 mWm-2 (Eckstein and
Simmons, 1978) west of the basin. These values are very similar to the uniform heat flow
measured in the eastern Mediterranean (Erickson, 1970). Consequently, the surface heat flow Q0
of 40 ± 2 mWm-2 we used to compute the equilibrium geotherm appears to be well constrained.
The surface temperature T0 was set in the model at 5 ºC. Regarding the first layer, PlioPleistocene to recent sediments are composed of fluviatile and lacustrine clastics, marls, chalks
and evaporites. The few quaternary conductivities available in the Dead Sea basin (Eckstein and
Simmons, 1978) are very low (1.25 Wm-1K-1) but were measured through only the first 150 m
15
from the surface. In order to get a brittle to ductile transition around 30 km with a surface heat
flow of 40 mWm-2, a mean thermal conductivity of at least 2.1 Wm-1K-1 is required in the first
layer. This figure appears as a realistic value taking into account compaction and a content of 510 percent of highly conductive evaporites in the first layer. It is unlikely that the true value over
the thickness (4.7 km) of the first layer would be lower than 2.0 Wm-1K-1.
The radiogenic heat generation rate is poorly constrained in the Dead Sea region. However,
about 110 m of recent sediments from two cores (Stiller et al., 1985) taken in the Dead Sea lake
contained on the average 3.87 ppm of 238U, 4.15 ppm of 232Th and 1.1 ppm of 40K. These U and
Th values are within the normal range of sedimentary materials found worldwide (Rodgers and
Adams, 1969). For layers 1 and 2 of density 2,150 kgm-3 and 2,550 kgm-3, the total heat
generation rate A is then (Beardsmore and Cull, 2001) 1.0 and 1.2 µWm-3 respectively. For the
crustal plutonic rocks of the model, we used the relations between the velocity of P waves Vp and
the heat generation rate A of Rybach and Buntebarth (1984). With their relation for Phanerozoic
rocks, we obtained (at 200 MPa) 2.27 and 1.27 µWm-3 for layer 3 (granite) and layer 4 (quartz
diorite) respectively. To account for the fact that the last stage of major regional plutonism
occurred (Garfunkel, 1999) during late Proterozoic (Pan-African orogeny), we applied an
arbitrary correction of -20 % to the computed values. The adopted heat generation rates for
layers 3 and 4 are then 1.8 and 1.0 µWm-3 respectively. For layer 5 (diabase), the RybachBuntebarth relation for Precambrian rocks led to a value of 0.2 µWm-3. An average value of
0.007 µWm-3 (Ranalli, 1987) was adopted for the upper mantle.
A frictional (brittle) failure criterion following Byerlee’s law of friction (Byerlee, 1968, 1978)
can be expressed from Anderson’s theory of faulting (Anderson, 1951) as (Sibson, 1974; Ranalli,
1987)
σ 1 − σ 3 = αρ gz (1 − λ )
(2.3)
where σ1 - σ3 is the failure stress, α a parameter depending on the type of faulting, ρ the average
density, g the acceleration of gravity, z the depth, and λ is the ratio of pore fluid pressure to
lithostatic pressure. For a friction coefficient of 0.75, values of the fault parameter α are 3.0, 1.2
and 0.75 for thrust, strike-slip and normal faults respectively (Sibson, 1974; Ranalli, 1987). We
adopted an intermediate value α of 1.05 between strike-slip and normal faulting as earthquake
focal mechanisms (van Eck and Hofstetter, 1989) and seismic reflection profiles (ten Brink and
Ben-Avraham, 1989) show that both types of faults coexist in the basin. The average density ρ in
the model is 2,670 kgm-3 for the crust, and 3,370 kgm-3 (Turcotte and Schubert, 2002) for the
upper mantle above the 220 km discontinuity. The pore fluid pressure was set at an intermediate
16
value between hydrostatic and dry. Equation 2.3 provides a lower limit to the failure stress
because it assumes an ideal orientation of faulting with respect to the stress field.
Ductile deformation in the crust is dominated by power-law creep (dislocation climb) given (e.g.
Ranalli, 1987) by
1
⎛ ε& ⎞ n C
σ 1 − σ 3 = ⎜ ⎟ e nRT
⎝D⎠
E
(2.4)
where σ1 - σ3 is the flow stress for a given strain rate, ε& the strain rate, D the Dorn parameter, n
the stress exponent, EC the creep activation energy, R the gas constant, and T is the temperature.
Values for D, n and EC are provided in Table 2.2.
Table 2.2 Dislocation climb (power-law) creep parameters
Rock / Mineral
Quartzite (wet) 1
Granite
1
Quartz diorite 2
Diabase
3
Olivine 4
Layer
D (Pa-n s-1)
n
EC (kJ mol-1)
1, 2
3.99 × 10-18
2.3
154
3
-29
7.92 × 10
3.2
123
4
5.02 × 10-18
2.4
219
5
-25
8.04 × 10
3.4
260
6
7.00 × 10-14
3.0
511
D is the Dorn parameter, n the stress exponent and EC is the creep activation energy.
From Ranalli and Murphy (1987), data from compilation of Kirby (1983).
2
From Kirby (1983), data from Hansen and Carter (1982).
3
From Kirby (1983), data from Shelton and Tullis (1981).
4
From Goetze (1978).
1
In the mantle, ductile deformation is controlled by the power-law creep (equation 2.4) of olivine
only for deviatoric stresses below 200 MPa. For deviatoric stresses greater than 200 MPa, the
glide-controlled creep of olivine is assumed to dominate (Goetze, 1978; Kameyama et al., 1999):
1
⎛
⎞
.
2
⎡
⎤
⎛
⎞
⎜
⎟
RT ⎜ ε 0 ⎟ ⎥
σ 1 − σ 3 = σ 0 ⎜1 − ⎢
ln .
⎟
⎜ ⎢ E p ⎜⎝ ε ⎟⎠ ⎥ ⎟
⎦ ⎟
⎜ ⎣
⎝
⎠
(2.5)
In equation 2.5, σ0 is the Peierls reference stress, Ep the activation energy for the Peierls
mechanism, and ε&0 is the reference strain rate. Values for σ0, Ep and ε&0 are provided in Table
2.3.
17
Table 2.3 Dislocation glide creep parameters
Rock / Mineral
Layer
σ0 (Pa)
Olivine
6
8.5 × 109
ε&0
(s-1)
5.7 × 1011
Ep (kJ mol-1)
535
σ0 is the Peierls reference stress, Ep the activation energy for the Peierls mechanism,and ε&0 is
the reference strain rate. Data from Goetze (1978).
A strain rate ε& of 2 × 10-15s-1 was used in the model. This value was derived from a relative
plate motion of 5 mm/yr, an intermediate value between short-term global positioning results of
2.6 ± 1.1 mm/yr (Pe’eri et al., 2002) and long-term geological estimates of 6-10 mm/yr
(Quennell, 1958; Freund, 1965).
At a given depth, the smaller value of the failure stress and the flow stress gives the yield
strength. A rheological profile (strength envelope) is a curve of yield strength versus depth. At
low temperatures, the failure stress is lower than the flow stress and brittle behavior dominates
the deformation of rocks. The opposite is true at high temperatures where aseismic ductile
behavior prevails. The usually sharp brittle to ductile transitions in the lithosphere are supposed
to correspond to boundaries of seismogenic zones. Several brittle to ductile transitions and
related seismogenic zones can occur in the lithosphere. The interpretation of strength profiles is
based on rather strong assumptions (Scholz, 2002) but the method provides a useful first-order
estimate of the rheology.
Figure 2.10 displays the results with a surface heat flow of 40 mWm-2 and a thermal
conductivity of 2.1 Wm-1K-1 in the first layer. A narrow brittle to ductile transition occurs in the
crust around 380°C at 31 km depth. With a heat flow of 42 mWm-2 and a conductivity of 2.0
Wm-1K-1 in the first layer, the transition would occur around 390°C at a depth of 26 km.
However, parameters we adopted from Shelton and Tullis (1981) for diabase in the lower crust
do not represent dry deformation conditions, as their samples were only dried at 160ºC. A recent
experimental study on the creep of diabase (Mackwell et al., 1998) revealed that this type of rock
is significantly stronger under truly dry conditions. Consequently, if the lower crust under the
Dead Sea basin has a basaltic composition and is dry, it should even be ductilely stronger than
what we report. In that case, no brittle to ductile transition would occur at all in the lower crust
except for unrealistic Moho temperatures above 600ºC and related surface heat flows greater
than 55 mWm-2. In the upper mantle, the brittle to ductile transition occurs in the model at 44
km depth and at 490ºC but as said earlier, the upper mantle appears to be aseismic during the 14year data period.
18
Temperature (C)
0
(a)
Temperature (C)
Strength (MPa)
0
100 200 300 400 500 600 700 800
0
0
L3
15
L4
K = 2.4
A = 1.0
Upper Crust
20
Lower Crust
Diabase
25
L5
K in Wm-1K-1
A in µWm-3
30
25
K = 2.1
A = 0.2
50
60
L6
70
70
80
80
90
20
40
K = 3.4
A = 0.007
90
Mantle
100
100
110
110
120
120
130
30
130
K in Wm-1K-1
A in µWm-3
140
140
150
0
100 200 300 400 500 600 700 800
Temperature (C)
150
0
500
Temperature (C)
Strength (MPa)
Depth (km)
Quartz Diorite
50
Depth (km)
Depth (km)
15
30
Peridotite
60
(b)
20
Moho
40
K = 2.8
A = 1.8
Crust
L1-L5
30
10
Granite
1500
0
10
20
Mesozoic to Miocene
K = 2.5 A = 1.2
10
1000
10
5
L2
500
0
Plio-Pleistocene to Recent
K = 2.1 A = 1.0
L1
5
Strength (MPa)
1000
1500
Strength (MPa)
Figure 2.10 Rheology of the Dead Sea basin. (a) Crustal geotherm (gray) and strength profile (black). (b)
Lithospheric geotherm (gray) and strength profile (black). Surface heat flow of 40 mWm-2. K is the thermal
conductivity and A is the radiogenic heat production rate.
2.5 DISCUSSION AND CONCLUSIONS
In the Dead Sea basin, well-constrained microearthquakes (ML ≤ 3.2) display continuous focal
depths down to the Moho located at a depth of 32 km. Sixty percent of these well-constrained
microearthquakes nucleated at depths of 20-32 km and more than 40 percent occurred below the
depth of peak seismicity situated at 20 km. An upper bound uncertainty of ± 5 km is estimated
for depths greater than 20 km, but depth mislocations should not exceed ± 2 km for most
earthquakes. No data support the view that lower-crustal seismicity could be nothing more than
an artifact due to earthquakes actually nucleating in the upper crust or in the upper mantle. Due
to uncertainties on focal depths, a few earthquakes might well have nucleated in the upper mantle
but a distinct population of upper mantle earthquakes is missing.
19
Most parameters in rheological modeling are commonly poorly constrained, and the method
itself suffers from inherent limitations (Scholz, 2002). Therefore, strength envelopes generally
cannot serve to accurately estimate the thickness of the seismogenic zone. In the case of the
Dead Sea basin, we are merely able to say that a brittle to ductile transition around 31 km depth
(where semi-brittle failure would prevail) is consistent with a surface heat flow of 40 mWm-2.
The low value of the regional surface heat flow is a good indication that the lower crust might be
cool and brittle. Nevertheless, since conductive thermal anomalies can take millions of years to
reach the surface, the surface heat flow does not always reflect lower-crustal temperatures. With
such a clear lower-crustal seismicity as the one monitored in the Dead Sea basin, a significant
departure from the equilibrium geotherm is however not expected. It appears therefore valid to
use the equilibrium geotherm to extrapolate temperatures to lower-crustal depths. The estimated
temperature of 380°C at the brittle to ductile transition is clearly below the temperature of 450°C
(350 ± 100°C) generally considered (Chen and Molnar, 1983) as the limiting temperature of the
deepest crustal seismogenic zone. In addition, a crustal seismic investigation of the Afro-Arabian
rifts (Prodehl et al., 1997) shows that upper mantle Pn velocities close to 8.0 km/s as found under
the Dead Sea (Ginzburg et al., 1981) are more typical of cooler rift flanks than of rifts axes,
where slower velocities are usually observed due to anomalous heating. If brittle behavior is then
likely to be the dominant deformation mechanism in the lower crust of the basin, strong
earthquakes should also nucleate in the lower crust and not only microearthquakes as we report.
Unfortunately, due to the long recurrence interval of strong earthquakes in the Dead Sea
(Shapira, 1997), several centuries of monitoring might be required before valid statistics would
allow a reliable assessment of this likely possibility. As an alternative solution to a brittle lower
crust, a model recently developed by Al-Zoubi and ten Brink (2002; ten Brink, 2002) suggests
that crustal flow might well be a viable deformation mechanism in the lower crust of the Dead
Sea basin. Although this is not what our results mostly suggest, it remains a possibility with a
higher heat flow and a lower crust made of wet diabase, or if quartz diorite substitutes for
diabase. Around 400°C, a dry diabase would be ductilely too strong and brittle failure would
prevail.
If the lower crust of the Dead Sea is cool and brittle, then the upper mantle should also be in a
seismogenic state but appears to be aseismic during the 14-year data period. This apparent
paradox is in agreement with Maggi et al. (2000), Jackson (2002) and earlier studies (Banda and
Cloetingh, 1992; Cloetingh and Burov, 1996) regarding the general scarcity of events in the
upper mantle of continents. Cloetingh and Burov (1996) suggest a few possible explanations:
stress relaxation due to crust-mantle decoupling, strengthening of the uppermost mantle in
downward-bent rift basins and low or inhomogeneous horizontal intraplate stress. Finally, the
20
mantle lithosphere may also not be so ductilely strong as suggested by laboratory experiments.
This last explanation is adopted by Maggi et al. (2000) and Jackson (2002), following the
observation (McKenzie and Fairhead, 1997; Maggi et al., 2000) that the effective elastic
thickness Te of the continental lithosphere is usually close to the thickness of the seismogenic
crust Ts. Consequently, the mantle would have no significant strength. In the case of the Baikal
rift, an effective elastic thickness Te larger than the total crustal thickness leads Déverchère et al.
(2001) to a different conclusion. The authors argue that on the contrary, the high strength of the
mantle is the reason explaining the scarcity of earthquakes below the Moho. The upper mantle
would not be aseismic but nucleation of earthquakes would be difficult, leading to long
recurrence intervals. In the case of the Dead Sea basin, we do not see decoupling between the
crust and the mantle as a likely mechanism explaining the absence of earthquakes in the upper
mantle, our results pointing towards a mechanically coupled crust-mantle. Unfortunately, this is
the only data-driven conclusion we can reach so far about this difficult and controversial subject.
Earthquakes between Aqaba-Elat and the Sea of Galilee were also relocated with the same
requirements and velocity model used to derive the distribution of depths in the Dead Sea basin.
According to the distribution of focal depths (Figure 2.2), the Dead Sea Transform is not
accompanied by any crustal thermal anomaly between the Dead Sea basin and the Sea of Galilee.
In this region, deep-crustal seismicity is not only observed along the Dead Sea Transform but
also along the Carmel fault zone off the Transform. Southward, the deepest earthquakes quickly
become shallower, and barely reach the lower crust in the region of Aqaba-Elat. With
appropriate adjustments in rheological models, the maximum depth of approximately 20 km in
this region is consistent with the surface heat flow of 65 mWm-2 measured in the northern part
of the Gulf of Aqaba-Elat (Ben-Avraham and Von Herzen, 1987). The thinning of the
seismogenic zone in the region of Aqaba-Elat is probably related more to the increase in the
regional heat flow toward the Red Sea (Ben-Avraham and Von Herzen, 1987) than to a heat
anomaly directly associated with the Dead Sea Transform itself.
ACKNOWLEDGMENTS
We thank S. Wdowinski for his help during the early stage of rheological modeling. We
benefited from stimulating discussions with M. Steckler and S. Feinstein. We are also thankful to
Uri ten Brink, Sierd Cloetingh, an anonymous reviewer, and the editor Scott King for their indepth criticism and advice. F.A. was supported by a Ph.D. grant from the Ministry of Energy and
Infrastructure of Israel.
21
Chapter 3
Methods of a new picking system: MannekenPix
The ability to perform accurate automatic phase picking on a broad range of data remains a
serious challenge facing the seismological community. The difficulties involved are somewhat
masked by the fact that picking is routinely done just by visual inspection of seismograms. The
best picking system widely recognized as such remains the human analyst. But analysts are slow,
and sometimes they scamp work due to the boredom induced by the highly repetitive nature of
onset picking, especially during periods of intense seismic activity. Analysts also frequently
introduce systematic errors due to inadequate working procedures. For instance, such errors can
result from the interaction between the picking process and the location results. If the location
algorithm does not include distance and residual weighting, chances are that analysts sometimes
move accurate picks closer to the predicted arrival in order to reduce the r.m.s. residual time of
the computed source locations. As an alternative or complementary mispractice, weights are
unduly downgraded at stations affected by high residual arrival times. Sometimes, analysts do
not zoom into seismograms (Douglas et al., 1997) to clearly resolve individual samples because
of time constraints. Time constraints can also imply that a great deal of seismograms remains
unpicked, especially in aftershock sequences and in swarms. Part of the data is then missing for
detailed studies. When the picking task is shared among several analysts, inconsistencies appear
unavoidable. Even a single analyst is likely to introduce them. It is sufficient to completely
repick a few times the same data set to notice many differences in arrival times and weights. If
the same exercise is performed annually, then the learning progress of the analyst over time also
reveals itself as a source of inconsistencies. The human learning capability, so desirable in itself,
comes unfortunately at the price of inconsistencies in the picking and weighting of phases. When
several analysts share the picking task as is often the case, their level of expertise is usually
uneven, and this makes inconsistencies unavoidable at all times. The highest level of
inconsistency is probably reached when data from several networks are merged. In that case,
22
heterogeneous picking methods, tools and policies add an ultimate layer of inconsistency to the
broader data set newly gathered. Inconsistencies can remain unnoticed when the main use of the
data is to locate events independently from each other, all phases of any particular event being
usually picked by a single analyst. When picking data from different analysts are blended
together in studies like joint hypocentral determination and travel-time tomography,
inconsistencies appear more clearly. Picking inconsistencies become more apparent as a
consequence of the high interaction between all the data in these joint studies. They can severely
jeopardize the meaning of the results. The only way to reduce inconsistencies for joint studies is
usually to completely revise the picking and the weighting of arrival times.
3.1 AUTOMATIC PICKING
After about thirty years of uncertain progress, a diffuse feeling is that automatic picking still
belongs to seismological gadgetry. But the need for high-quality automatic picking is real and
quickly growing. Detailed studies are usually performed years after the actual recordings,
involving sometimes millions of seismograms. As most of these studies require carefully picked
and weighted arrival times, other ways than manually re-picking huge amounts of data are highly
desirable. With the abundance of seismograms contaminated by poor practices, automated
alternatives are even of vital importance for the feasibility of a growing number of modern
seismic applications.
There are basically two main approaches to automated picking. A first way is to pick each
seismogram independently from the others and one event at a time. Single-trace picking can be
seen as an extension of the detection process, and some methods work in near-real time. It is also
the first way analysts usually try during the routine task of picking seismograms. Traditional
methods quantify some attributes of waveforms like amplitude, frequency or polarization, and
apply their detection and picking algorithms on these attributes or on a smoothed combination of
them. Among the wide variety of traditional methods for picking first arrival P-waves of local
and regional events, Allen (1978, 1982) designed a STA/LTA algorithm applied on an envelope
function sensitive to both amplitude and frequency of seismograms. Despite its age, Allen’s
picking system is still part of Earthworm (Johnson et al., 1994) and Sac2000 (Goldstein et al.,
1999). Baer and Kradolfer (1987) derived their picking engine from Allen’s work but they use
the square of a modified envelope to generate a characteristic function whose value is tested
against an adjustable threshold. The Baer-Kradolfer picker is integrated into Pitsa (Scherbaum
and Johnson, 1992). Autoregressive methods (Morita and Hamaguchi, 1984; Takanami and
23
Kitagawa, 1988; Kushnir et al., 1990; GSE/Japan/40, 1992; Takanami and Kitagawa, 2003) work
also well for picking local events, but they can also be used at regional and teleseismic distances
(Leonard and Kennett, 1999; Sleeman and van Eck, 1999). The Cusum algorithm (Basseville and
Nikiforov, 1993) appears as an attractive alternative to autoregressive methods at regional
distances (Der and Shumway, 1999; Der et al., 2000). Klumpen and Joswig (1993) apply pattern
recognition on polarization images for P- and S-onset picking of three-component local data.
Non-traditional methods like neural networks can sometimes work directly on seismograms (Dai
and MacBeth, 1995, 1997), avoiding the need to compute attributes or characteristic functions.
A second approach to automatic picking is to work on several seismograms at once, exploiting
the similarity of waveforms from nearby events. This multi-trace approach derives basically
from seismic refraction methods (Peraldi and Clement, 1972) used to compute static corrections
of seismic reflection data. In seismology, seismograms are typically organized in common
station gathers (Dodge et al., 1995; Shearer, 1997). A good account of the methodology and its
historical progress is provided by Aster and Rowe (2000). Joswig and Schulte-Theis (1993)
extended the application of master-event correlation by using dynamic waveform matching for
weak local events occurring in clusters.
The single-trace approach appears today to be more versatile than the multi-trace approach in the
sense that it is not based on the restrictive criterion of waveforms similarity. A multi-trace
approach is inherently better adapted to relatively restricted volume studies like those where
clusters usually occur. Aster and Rowe (2000) suggest however that further developments in
adaptive filtering and event clustering (Rowe et al., 2002) might significantly extend the range of
data sets that can benefit from cross-correlation picking techniques.
In order to perform appropriately on a wide range of data, I believe that picking algorithms
should be integrated into complete processing sequences consistent with the requirements of
target applications, where the picking results become the input data. Most picking algorithms
need the synergetic support of these complementary components before they can be turned into
robust production tools. Despite the impressive number of picking methods reported, the need
for complementary components has probably not received enough recognition in the literature.
Examples of such components are high-fidelity filters of seismograms, methods for estimating
time uncertainties associated with picked phases, and how the deconvolution by the instrumental
response could increase the accuracy of phase picking. Estimating picking uncertainties appears
to me as the second most important function of an automated system. In order to be meaningful,
every physical measurement needs an assessment about its own uncertainty. A valid phase pick
24
datum should then be understood as made of two quantities: first, the arrival time and second, the
uncertainty, both expressed in time units. Many picking algorithms do not tackle the uncertainty
estimation at all, or provide qualitative weights poorly tied to time uncertainties.
I think also that the literature has perhaps not done enough to convince potential users that
automatic picking can really solve some of their problems. Papers usually focus so much on
picking methods that a clear profile of the underlying data is often omitted. Potential users are
then unable to see the relation between the data from which the picking algorithms derive and
their own data and picking needs. With very few exceptions (Baer and Kradolfer, 1987; Sleeman
and van Eck, 1999; Leonard, 2000), comparative studies where several algorithms are applied on
a common data set are also missing, making it difficult to know which algorithms perform best,
and under which conditions. The lack of comparative studies means also that good results
obtained on one data set can be of very little meaning for other sets of data. Some tables
summarizing the results of various methods have well been made. Besides classifying the
methods involved, these tables do not allow meaningful comparisons as each method is
specifically tied to its own data set. On the other hand, it is also often not clear what kind of
benefits can be expected from automated picking and at what price. Finally, most users are not
willing to perform lengthy tests and related programming efforts for an uncertain result. Users
want turn-key solutions that work and these are very difficult to find. Automatic picking
capabilities are well integrated into Sac2000 (Goldstein et al., 1999), Pitsa (Scherbaum and
Johnson, 1992) and Seisan (Havskov and Ottemöller, 1999), but these packages do not specialize
in automatic picking. As such, they also require too much development and tuning efforts for
most users before a true production mode can be reached.
3.2 MANNEKENPIX
In order to automatically pick first arrival P-waves on single-component records, I developed a
program called MannekenPix. The main goal of the program is to provide picking data close in
quality and quantity to those of a good human analyst. Because MannekenPix was originally
developed to pick local events in the Dead Sea region where a great variety of waveforms is
observed, it follows the single-trace approach. This approach is of interest to the seismological
community because of its inherent versatility making it virtually applicable to a broad range of
data. MannekenPix has provided good results for local earthquakes from the Dead Sea region
(see Chapter 4), and for local - regional earthquakes from Italy (see Chapter 5). These results
indicate that the program is probably adaptive enough to satisfy the stringent requirements of
25
local and regional earthquake tomography for other data sets as well. From version 1.7,
MannekenPix is also able to tackle teleseisms but this capability has not yet been tested on a
sufficiently large data set.
The program works in guided mode. It searches for a valid arrival around the time of a manual
pick or around the time of a predicted value. This is a common setup for high-quality
seismological studies where data are selected from a catalogue of routinely located events
spanning several years. The presence of more than one event per record is also not uncommon
and makes it often desirable to guide the system in search of an arrival of interest. If no event
location is available to provide at least a predicted value, the program can also search around the
trigger time of a network detection algorithm. MannekenPix is a turn-key solution that does not
require much tuning from an experienced user before a true production mode can be reached.
The first benefit that can be expected from MannekenPix is picking accuracy. Most automatic
picks are comparable to those of a good human analyst. But as said earlier, the quality of the
picking is not only a function of the picking accuracy, it also depends on how well the picking
uncertainty is evaluated. MannekenPix includes a weighting mechanism rigorously calibrated on
reference picks and weights provided by the user. This calibration is best described as a learning
process by example. On unseen data, the weighting engine applies the knowledge gained during
the calibration to mark every picked arrival with a quality label. The weighting mechanism of
MannekenPix attempts to predict the same uncertainties as those that would be estimated by the
user. As such, it acts as an extension of the manual approach and not as a totally independent
method possibly in conflict with the legacy. The greatest benefit of the program, an improved
picking set, results however from its ability to avoid the mispractices and inconsistencies
accumulated by the analysts over the years.
As a side-effect of its own consistency, the program misses some arrivals from seismograms that
were picked manually. This can be a problem for events with very few phases because these
events might then become un-locatable. However, as tomographic studies usually discard events
with very few phases, this should be an affordable price to pay for studies involving great
amounts of data. The total number of automatically picked phases can be comparable to the
number of phases routinely picked because MannekenPix is usually able to compensate the
missed arrivals by picking some decent seismograms left unpicked by the analysts. If many
seismograms are routinely unpicked, then the number of seismograms picked by MannekenPix
can largely exceed the number of routinely picked seismograms.
26
In order to increase the signal-to-noise ratio of the P-wavetrain before picking, the seismograms
are filtered in the first step of MannekenPix by a high-fidelity Wiener filter. The picking is
performed in the second step by the robust and versatile Baer-Kradolfer (Baer and Kradolfer,
1987) picking engine. If a valid pick has been found, a variable delay correction is applied in the
third step in order to reduce the inherent delay of the Baer-Kradolfer algorithm arrivals. In the
fourth step, the weighting engine provides a statistical estimate of the picking uncertainty. For
each data set, the weighting engine has to be calibrated first by a multiple discriminant analysis
performed on user-supplied reference picks and weights.
3.3 THE FOUR STEPS OF MANNEKENPIX
The four steps of MannekenPix (Table 3.1) are the foundations of the program, and the methods
underlying these steps are reviewed in this section.
Table 3.1 The four steps of MannekenPix
Processing step
Pre-picking
1. Wiener Filter
Theory
Implementation
Statistical Signal Processing
F.A.
Univariate Statistics
Picking
2. Automatic Picking
Signal Processing
3. Delay Corrections
Baer-Kradolfer
Univariate Statistics
F.A.
Multivariate Statistics
F.A.
Post-picking
4. Weighting
I assume that one of the ultimate goals of automatic picking is to achieve the highest accuracy
possible. However, even the highest picking accuracy cannot prevent time base errors to directly
affect the total uncertainty on picked phases. Maintaining at all times an accurate time base
signal across a network of stations can be difficult, even with GPS timing technology. In a recent
LET study of the Ionian channel region in Greece, great efforts were required (Hasslinger, 1998)
to reduce time base uncertainties to ± 10-20 ms (with data sampled every 4 or 10 ms) on radio-
27
transmitted and GPS time signals of a dense temporary network. The total uncertainty affecting
picking arrivals has also to take into account these time base uncertainties, but this can be done
separately from the estimation of the picking uncertainties.
3.3.1 WIENER FILTER
Linear least-squares optimal filtering of stationary time series
Following Aki and Richards (1980), signal can be defined as the desired part of the data while
noise is the remaining and unwanted part. Signal and noise have thus a relative meaning as they
depend on the object of interest. The signal-to-noise ratio is not only affected by the level of
ambient ground noise it is also affected by the whole recording process, in which the
instrumental response plays an important role.
The attenuation of noise through selective frequency filtering has been widely and often wildly
used. Some raw filtering approaches are sometimes described as being optimal. It is improbable
that these raw approaches could be optimal in a mathematical sense. I do not mean that raw
filters are not useful, but rather that they cannot be optimal if they are not explicitly based on a
theory of optimal filters.
As part of the manual picking process, analysts commonly filter seismograms. But manually
adjusting corner frequencies and slopes of a filter is time-consuming, and a causal filter can
induce further delays in the visible onsets. On the other hand, a noncausal filter can create
precursory side-lobes if the corner frequencies and the slopes of the transition bands are not or
cannot be perfectly adjusted manually. Another common setup is to apply one common filter to a
complete data set. This can improve most seismograms if the filtering effect is mild but in that
case, the improvements might also be insufficient. If the filtering effect is stronger, then delays
or precursory side-lobes will unavoidably appear on some seismograms, and significant signal
attenuation can lead to late picking and polarity errors. As a result, frequency filtering is
sometimes simply discarded because the problems it introduces appear to outweigh the benefits.
Fortunately, optimal filtering methods exist.
The theoretical foundations of continuous time linear least-squares filters were laid by Norbert
Wiener in 1942 in a classified monograph. The work was published later in Interpolation,
Extrapolation and Smoothing of Time Series (Wiener, 1949). To avoid the transcendental
28
analysis of continuous time, N. Levinson worked out a discrete-time formulation of Wiener’s
theory that opened computational possibilities (Levinson, 1947a, 1947b). Today, Wiener filters
play an important role in a wide range of applications such as noise reduction, prediction,
deconvolution, channel equalization and system identification.
In the frequency domain, a filter output Sˆ ( f ) is the product of the filter frequency response
W ( f ) and the total input frequency response T ( f ) :
Sˆ ( f ) = W ( f )T ( f ) .
(3.1)
The filter error E ( f ) is defined as the difference between a desired signal S ( f ) and the filter
output Sˆ ( f ) :
E ( f ) = S ( f ) − Sˆ ( f ) .
(3.2)
The mean-square error ξ of the filter is then
ξ =E
{
E( f )
2
}
(3.3)
with E being the expectation.
A Wiener filter is a linear operator designed to minimize the mean-square error (3.3) between the
filter output and a desired signal. In their basic form, Wiener filters assume that signal and noise
are wide-sense stationary (WSS) random processes. If signal and noise are Gaussian time series,
then the Wiener filter is an optimal estimator and it is also optimal among all non-linear
estimators. This property is not true for non-Gaussian signal and noise.
It can be shown (Hayes, 1996; Vaseghi, 2000) that the minimum mean-square error Wiener filter
in the frequency domain is given by
W( f ) =
PS ,T ( f )
PT ,T ( f )
(3.4)
where PS ,T ( f ) is the cross-power spectrum between the signal S ( f ) and the total input T ( f ) ,
and PT ,T ( f ) is the power spectrum of the total input T ( f ) .
In the case of a signal S ( f ) buried in additive noise N ( f ) , the total input T ( f ) is then
T ( f ) = S( f ) + N ( f ) .
(3.5)
Assuming that the signal S ( f ) and the noise N ( f ) are uncorrelated, we can write
PS ,T ( f ) = PS ,S ( f )
29
(3.6)
and
PT ,T ( f ) = PS ,S ( f ) + PN , N ( f )
(3.7)
where PS ,S ( f ) is the power spectrum of the signal and PN , N ( f ) is the power spectrum of the
noise. The Wiener filter in the case of uncorrelated additive noise is then given by
W( f ) =
PS ,S ( f )
PS ,S ( f )
=
.
PT ,T ( f ) PS ,S ( f ) + PN , N ( f )
(3.8)
From equation (3.8), the Wiener filter for noise reduction is often described as a S 2 /( S 2 + N 2 )
filter. The amplitude of W ( f ) will be close to 1 for frequencies where the noise is negligible,
and close to 0 where the noise is dominant. The intermediate values given by (3.8) are the
optimal way of filtering the noise (maximize the SNR) between the two extremes. As a
consequence of the linear framework, phase angles of signal and noise are not used (Bode and
Shannon, 1950) in Wiener filters.
It can be further shown (Press et al., 1986; Hayes, 1996) that equation (3.8) remains valid if the
desired signal is not the recorded signal S ( f ) , but the true original signal S0 ( f ) unaffected by
the instrumental response. In that case, the filtering problem can be solved first for the estimated
recorded signal Sˆ ( f ) , leading from equations (3.1) and (3.8) to
Sˆ ( f ) =
PS ,S ( f )
T( f ) .
PS ,S ( f ) + PN , N ( f )
(3.9)
The estimate Sˆ0 ( f ) of the true original signal S0 ( f ) is then
Sˆ ( f )
Sˆ0 ( f ) =
R( f )
(3.10)
where R( f ) is the impulse response of the recording system. The full Wiener filter is then made
of frequency filtering (3.9) followed by deconvolution (3.10). The frequency filtering regularizes
the deconvolution by suppressing the noise at frequencies where it dominates the signal, and it
only requires the power spectrum of the recorded signal S ( f ) , not the power spectrum of the
true original signal S0 ( f ) .
In seismology, removing the response of the recording system is usually performed for the
determination of ground motion amplitudes, and not for picking purposes. However,
deconvolving the instrumental response is part of the full Wiener filter and it might become an
advanced tool in search for the most accurate onsets of seismic phases, whether picked manually
or automatically. The high-frequency content of short-period seismograms might however
30
suggest that removing the response of the recording system is not worth the burden compared to
the potential accuracy recoverable. This might be true for the routine work but I think that
deconvolution should not be overlooked for high-accuracy studies.
The main problem with the recording system is that it usually distorts and lengthens significantly
the true ground motion, whether it be signal or noise. Such a systematic distortion does not only
mean that recorded waveforms do not accurately reflect the true shape of signals, it also implies
a reduction of the signal-to-noise ratio. The seismic recording system acts as an out-of-focus lens
through which everything appears blurred, even in the absence of additive noise. On most
seismograms, the amplitude of the first samples of seismic phases is so low that true onsets are
nearly always obscured by some residual noise. This contrasts with the sharp initial rise
suggested by source models, especially when the data are recorded by short-period seismometers
mainly sensitive to velocity. This problem leads some analysts to systematically and often
arbitrarily pick earlier than the onsets they really see. Under these circumstances, accurately
picking seismic phases appears to be rather illusory. A synthetic example will show that the
instrumental response can explain a great deal of the blur observed, even for noiseless
seismograms. Deconvolution would then be the way to refocus the smeared signals. If widely
applicable to real-world data within the scope of phase picking, deconvolution could
significantly increase the accuracy of single-trace picking and reduce related uncertainties.
Stochastic and data-adaptive Wiener filters
In their initial form, Wiener filters are based on ensemble averages as in equation (3.3), and one
filter is applied to all realizations of a given process. This approach is called stochastic by
Berkhout and Zaanen (1976). Models for the noise and for the signal are required. As a second
approach and under the assumption that ensemble averages can be approximated by time
averages, Wiener filters can also be data-adaptive or deterministic. They can then be tailored to
specific realizations where the statistical properties of the signal and noise are directly estimated
from the data. While background noise is often almost stationary over short segments of time,
seismic signals are transients. It is clear then that strict stationarity of noise and signal cannot be
expected from seismograms. One way to apply Wiener filters is to restrict their use or validity to
data segments where signal and noise are almost stationary. In the framework of guided phase
picking where an arrival is constrained to occur within some time window, segmented
stationarity is usually applicable.
31
Among the few Wiener filters for noise reduction described in the seismological literature,
Douglas (1997) follows the stochastic approach and computes the filter in the time domain
according to Franklin’s method (1970). In the presence of errors, the linear inverse problem can
be written as
As + n = t
(3.11)
where s is the unknown, t the observation, n the error vector, and A is the coefficient matrix
relating s and t. In the case where t is a sampled times series containing a signal s buried in
additive uncorrelated noise n, A is the identity matrix and the Wiener filter w is given in the time
domain by
w = R s ,s ⎡⎣ R s ,s + R n ,n ⎤⎦
−1
(3.12)
where R s ,s is the autocorrelation matrix of the signal and R n ,n is the autocorrelation matrix of
the noise. The similarity between (3.8) and (3.12) results from the Wiener-Kintchine theorem
(Wiener, 1930; Kintchine, 1934) stating that autocorrelation and power spectrum are Fourier
transforms of each other. The estimate ŝ of the signal s is then given by
−1
sˆ = R s ,s ⎡⎣ R s ,s + R n ,n ⎤⎦ t .
(3.13)
In order to filter only the low-frequency part of the noise, Douglas uses a tapered cosine wave of
the predominant noise period as model for the noise, and the impulse response of the recording
system as model for the signal. The author expresses his preference for filters derived from
models over data-adaptive filters. First, a great number of data points are required to obtain
detailed and reliable autocorrelations of noise segments, and stationarity becomes an issue for
autocorrelations derived from long data segments. When only a small number of points is used,
the resulting filter has a smooth response and the detailed features of the noise sample are lost.
Data-adaptive filters thus add complexity for little advantage. Further, the smoothness of filters
derived from models helps in reducing the number of artifacts on the filtered seismograms.
The Wiener filter of MannekenPix is however data-adaptive, signal and noise power spectra in
(3.8) being automatically estimated from the data for each seismogram. A first window located
ahead of the a priori arrival time samples the noise, while part of the noisy P-wavetrain is
sampled by a second window located after the arrival. Assuming as before that the signal and the
noise are uncorrelated, the power spectrum PSN ,SN ( f ) of the noisy signal SN ( f ) is then
PSN ,SN ( f ) ≈ PS ,S ( f ) + PN , N ( f )
32
(3.14)
and approximates thus the denominator of the Wiener filter (3.8). The numerator of the filter (the
power spectrum PS ,S ( f ) of the signal) can be estimated by subtracting the power spectrum
PN , N ( f ) of the noise from (3.14). The Wiener filter of MannekenPix can then be written as
W( f ) =
PS ,S ( f )
P
( f ) − PN , N ( f )
≈ SN ,SN
.
PS ,S ( f ) + PN , N ( f )
PSN ,SN ( f )
(3.15)
The main difference between Douglas stochastic filter and the data-adaptive filter of
MannekenPix is that the scope of the later is broader compared to the former. Douglas filter
attenuates only the low-frequency noise and considers the signal to be highly impulsive in all
cases. While these sensible assumptions can help to reduce artifacts, they might also be too
restrictive. Recorded seismic signals are rarely impulsive enough to fill the bandwidth of the
recording system, and high-pass filtering is then not always sufficient. By adapting itself to the
frequency content of each seismogram, the Wiener filter of MannekenPix acts as a high-pass, a
low-pass, a band-pass, a notch filter, or any meaningful combination of these primitives. Picking
routines such as the Baer-Kradolfer algorithm highly amplify both amplitude and frequency
changes of seismograms. Any frequency dominated by noise should then be attenuated as much
as possible, whether it be noise located in a single band of frequencies or in multiple bands.
Douglas objection against such detailed filters results from the apparent impossibility to satisfy
both practical stationarity (as with short data segments) and high resolution (as with long data
segments). But solutions to this old problem are already known for more than thirty years and
they cannot be ignored today.
Power spectrum estimation
By virtue of the Wiener-Kintchine theorem (Wiener, 1930; Kintchine, 1934) stating that
autocorrelation and power spectrum are a Fourier transform pair, estimating the power spectrum
is equivalent in the frequency domain to estimating the autocorrelation in the time domain. In
theory, all that must be done then is to compute the autocorrelation and take its Fourier
transform. However, there are two difficulties with this direct approach. First, practical
stationarity of both the noise and the transient seismic signal requires the use of short data
segments but detailed and reliable spectra are difficult to derive from short segments. The second
difficulty is that estimating power spectra of real-world data is always done in a noisy
environment directly affecting the results.
33
The numerous methods for power spectrum estimation are generally categorized into at least two
main classes. The first class includes classical or nonparametric methods, in which the power
spectrum is directly estimated from the data. Classical methods differ mainly in the way they
window the data or the autocorrelation before taking a Fourier transform. They are also
sometimes referred to as linear methods because they only involve linear operations, and their
window functions are independent of the data. The second class includes nonclassical or
parametric methods, in which the data are assumed to be the output of a linear system driven by
white noise. Parametric methods are based on a model for the process generating the data. They
are said to be nonlinear because their window functions are data-adaptive. The maximum
entropy method (MEM) appears as a logical first stop in the world of parametric methods since
its main properties for 1-D spectral analysis (MEM1) are rather well established both
theoretically and experimentally (Wu, 1997), and numerous implementations of the method are
readily available.
Classical methods are more general than parametric methods since they do not incorporate
information about the process that generated the data. In some applications however, this may be
an important limitation. In speech processing, an acoustic model for the vocal tract imposes an
autoregressive model on the speech waveform (Rabiner and Schafer, 1978). For short intervals
of time over which the speech waveform is approximately stationary, a parametric approach
based on an autoregressive model could then provide a more accurate estimate of the power
spectrum than a nonparametric method.
Classical methods of power spectrum estimation
The existence of numerous classical methods for spectral estimation results mainly from attempts
to overcome the inherent limitations of the Periodogram, a method first introduced by Schuster
(1898) in his study of periodicities in sunspot numbers. For a discrete signal x ( n ) of length N,
the periodogram PˆX , X ( f ) is proportional to the squared magnitude of the discrete Fourier
transform (DFT) of x (n ) and is given (e.g. Hayes, 1996) by
1
2
PˆX , X ( f ) =
X( f )
N
(3.16)
where X ( f ) is the N-point discrete Fourier transform (DFT) of x (n )
N −1
X ( f ) = ∑ x ( n )e − j 2π nf .
n=0
34
(3.17)
With respect to the autocorrelation, a finite segment of data behaves as an infinite series
multiplied by a Bartlett (triangular) window. Multiplication in the time domain by the Bartlett
window corresponds to a convolution in the frequency domain by the Fourier transform of the
Bartlett window. The periodogram is a biased estimate of the power spectrum and its expectation
is given by
{
}
E PˆX , X ( f ) = PX , X ( f ) * WB ( f )
(3.18)
where PX , X ( f ) is the true power spectrum, “*” denotes convolution, and WB ( f ) is the Fourier
transform of the Bartlett window, converging to an impulse as N goes to infinity. The
periodogram is then asymptotically unbiased
{
}
lim E PˆX , X ( f ) = PX , X ( f ) .
N →∞
(3.19)
For white Gaussian noise, the variance of the periodogram is proportional to the square of the
power spectrum
{
}
Var PˆX , X ( f ) ∝ PX2 , X ( f )
(3.20)
and does not go to zero as N goes to infinity. The periodogram is thus not a consistent estimate of
the power spectrum.
Figure 3.1 displays the periodogram power spectral density (PSD) of a noiseless harmonic
signal, computed with function “periodogram” of Matlab Signal Processing Toolbox. This
periodogram derives from a long data segment encompassing more than 50 periods of the
monochromatic signal. The same signal will serve to illustrate the main properties of other
widely used methods of estimating power spectral densities. A one-sided PSD means that the
integrated power spectral density over only positive frequencies equals the total power (meansquare amplitude) of the data segment. In order to increase the number of points in the frequency
domain, the data segment was zero padded up to a total of 2,048 points by the “FFT” function of
Matlab. There are then (2,048 / 2) + 1 = 1,025 frequencies on the positive axis between 0 Hz and
the Nyquist frequency (50 Hz), and the frequency sampling period is 0.0488 Hz. Due to the
Bartlett window inherent of the periodogram, significant power is transferred (spectral leakage)
to the whole range of frequencies. In addition, the smoothing introduced by windowing broadens
spectral features and hence reduces resolution. In the example, the main lobe at 20.5 Hz is 0.55
Hz wide at the 10-percent level of the peak value.
Even with such a long data segment as the one of the example, the periodogram suffers thus a
rather poor resolution and a high spectral leakage. It does not appear well suited for analyzing
closely-spaced sinusoids (due to low resolution) and continuous spectra (due to high leakage). In
35
Frequency (Hz)
10
15
20
25
30
103
40
45
50
V (t ) = 10sin(2π 20.5t )
102
PSD (volt2/ Hz)
35
103
102
101
101
100
100
10-1
10-1
10-2
10-2
10-3
10-3
10-4
10-4
10-5
10-5
0
5
10
15
20
25
30
35
40
45
2
5
PSD (volt / Hz)
0
50
Frequency (Hz)
Figure 3.1 One-sided periodogram of a 20.5 Hz harmonic potential difference V(t) of 10 volts peak amplitude. 256point data segment, 0.010 sec sampling period, and 2,048-point FFT.
addition, bias and resolution further degrade when short data segments are used. This is
especially important in our case since we need spectra derived from short windows in order to
ensure practical stationarity of the data segments used to estimate the Wiener filter.
For any finite data segment of N samples, the number of samples available for the estimation of
the autocorrelation value rˆx , x ( k ) at lag k, is very low as k approaches N. Therefore, the estimate
of the autocorrelation at lag k when k is close to N, is always unreliable and the variance of the
entire autocorrelation estimate increases. In the Blackman-Tukey method (1958), also referred to
as periodogram smoothing, the variance is reduced by applying a (correlation lag) window to the
autocorrelation estimate before taking its Fourier transform. What is traded for this reduction in
variance, however, is a reduction in resolution since a smaller number of (and now unequally
weighted) lags is used to estimate the power spectrum.
Figure 3.2 displays the Blackman-Tukey method PSD of the example signal, computed with
Matlab code from Hayes (1996). A 384-point wide Blackman lag window produced a smooth
spectrum, but the 20.5 Hz peak is now 1.25 Hz wide at the 10 percent level. In this method, the
Blackman-windowed autocorrelation is computed using only the 256 available data points, and
this lagged autocorrelation is then zero padded when the FFT is taken.
36
Frequency (Hz)
5
10
15
20
25
35
40
45
50
103
V (t ) = 10sin(2π 20.5t )
102
102
101
101
100
100
10-1
10-1
10-2
10-2
10-3
10-3
10-4
10-4
10-5
10-5
2
PSD (volt / Hz)
30
0
5
10
15
20
25
30
35
40
45
PSD (volt2/ Hz)
0
103
50
Frequency (Hz)
Figure 3.2 One-sided Blackman-Tukey method PSD of a 20.5 Hz harmonic potential difference V(t) of 10 volts
peak amplitude. 256-point data segment, 0.010 sec sampling period, 2,048-point FFT, and 384-point Blackman
window (its shape is in the upper-right corner). The periodogram is shown in gray for comparison.
In Thomson’s Multitaper method (Thomson, 1982; Park et al., 1987; Percival and Walden,
1993), a small number of leakage-resistant tapers is applied to a single time series from which
several spectra are produced. The tapers, known as discrete prolate spheroidal sequences
(DPSS), are constructed so that each taper samples the time series in a different manner while
optimizing resistance to spectral leakage. The statistical information discarded by the first taper
is partially recovered by the next taper, and so on. Averaging over this small ensemble of spectra
reduces the variance compared to single-taper methods. In the multitaper method, the timebandwidth product parameter NW allows to balance the tradeoff between variance and
resolution. There are 2 NW – 1 tapers used, so that when NW increases, there are also more
estimates of the power spectrum and the variance of the averaged estimate decreases. However,
the bandwidth of each taper is also proportional to NW and spectral leakage increases as NW
increases.
Figure 3.3 displays the Multitaper method PSD of the example signal, computed with Matlab
code from P.J. Huybers1. The time bandwidth product NW was set at 1.5, resulting in only 2
DPSS tapers. The 20.5 Hz peak is 1.15 Hz wide at the 10 percent level, only slightly narrower
1
http://web.mit.edu/phuybers/
37
Frequency (Hz)
5
10
15
20
25
30
35
40
45
50
V (t ) = 10sin(2π 20.5t )
0
5
10
15
20
25
30
35
40
45
103
102
101
100
10-1
10-2
10-3
10-4
10-5
10-6
10-7
10-8
PSD (volt2/ Hz)
2
PSD (volt / Hz)
0
103
102
101
100
10-1
10-2
10-3
10-4
10-5
10-6
10-7
10-8
50
Frequency (Hz)
Figure 3.3 One-sided Multitaper method PSD of a 20.5 Hz harmonic potential difference V(t) of 10 volts peak
amplitude. 256-point data segment, 0.010 sec sampling period, 2,048-point FFT, and NW = 1.5 (2 tapers). The
periodogram is shown in gray for comparison.
than with the Blackman-Tukey method, but spectral leakage appears significantly reduced
compared to previous methods.
The Maximum Entropy Method (MEM)
A serious limitation of classical methods to power spectrum estimation is that, for a data segment
of length N, the autocorrelation rx , x ( k ) can only be estimated for k < N , and rx , x ( k ) is assumed
to be zero for k ≥ N . Since many signals have autocorrelations that are nonzero for lags
k ≥ N , this assumption often results in significant spectral leakage and loss of spectral
resolution. This is particularly the case for narrowband signals, for which autocorrelations decay
slowly with k. In general, there is an infinite number of autocorrelations that are identical to the
estimated autocorrelation of a data segment for lags k < N . Therefore, constraints must be
imposed on the set of possible extrapolations in order to provide a meaningful and unique
answer.
38
Given the autocorrelation rx , x ( k ) of a WSS process x ( n ) for k ≤ m , the problem is how to
extrapolate rx , x ( k ) for k > m . In the frequency domain, an extrapolated power spectrum
PX , X ( f ) can be written as
PX , X ( f ) =
m
∑r
k =− m
x,x
( k )e − j 2π fk +
∑ r ( k )e
k >m
− j 2π fk
e
(3.21)
where rx , x ( k ) is the data-derived autocorrelation, and re (k ) is the extrapolated autocorrelation.
First, PX , X ( f ) needs to be a valid power spectrum, and hence it should be real-valued and
nonnegative for all f. An additional constraint, proposed by Burg (1967), is to extrapolate the
autocorrelation in such a way as to maximize (Jaynes, 1957a, 1957b) the information entropy
(Shannon, 1948) of the process. Since entropy is a measure of randomness, a maximum entropy
estimate provides the autocorrelation sequence corresponding to the most random signal whose
correlation values for lags k ≤ m coincide with the measured values. Such an extrapolation
places as few constraints as possible or the least amount of structure on the process x (n ) .
For a Gaussian random process with power spectrum PX , X ( f ) , the entropy rate (e.g. Smylie et
al., 1973; Wu, 1997) is given by
1/ 2
1
H = ∫ ln PX , X ( f )df .
2 −1/ 2
(3.22)
For Gaussian processes with a given partial autocorrelation sequence rx , x ( k ) for k ≤ m , the
maximum entropy power spectrum is the power spectrum that maximizes equation (3.22) subject
to the constraint that the inverse discrete-time Fourier transform of PX , X ( f ) equals the partial
autocorrelation sequence rx , x ( k ) for k ≤ m ,
1/ 2
rx , x ( k ) =
∫
PX , X ( f )e j 2π fk df ,
k ≤m.
(3.23)
−1/ 2
The variational procedure leads to the Maximum Entropy Method power spectrum (Burg, 1967,
1975) PˆMEM ( f ) , given for a unit sampling by
PˆMEM ( f ) =
Pm +1
m
1 + ∑ amk e
2
(3.24)
− j 2π fk
k =1
where Pm+1 and the coefficients amk are given by the matrix equation
⎡ rx , x (0)
⎢ rx , x (1)
⎢M
⎢ rx , x ( m )
⎣
rx , x (1)
K rx , x ( m ) ⎤ ⎡1 ⎤ ⎡ Pm +1 ⎤
rx , x (0)
K rx , x ( m − 1) ⎥ ⎢ am1 ⎥ ⎢ 0 ⎥
⎥ ⎢M ⎥ = ⎢M ⎥ .
M
M
⎥ ⎢⎣ amm ⎥⎦ ⎢⎣ 0 ⎥⎦
rx , x ( m − 1) K rx , x (0)
⎦
39
(3.25)
Equation (3.25) is equivalent to the design of a ( m + 1) -point prediction error filter with mean
square error Pm+1 , and whose first coefficient is set equal to 1. van den Bos (1971) has shown
that the maximum entropy method is also equivalent to least-squares fitting of a discrete-time
autoregressive (all-pole) model (Yule, 1927) of some order M to the data. An order M
autoregressive process x(t ) with unit sampling can be written as
M
x (t ) = ∑ amk x (t − k ) + ξ (t )
(3.26)
k =1
where the white noise contribution ξ (t ) is usually called the innovation of the AR process. The
constants amk in equation (3.26) are the coefficients of the AR process and are solutions to the
matrix equation (3.25). The mean square error Pm+1 of the prediction error filter in equations
(3.24) and (3.25) corresponds, for the AR model, to the mean square value E (ξ 2 (t )) of the
innovation.
Several methods can be used to solve the linear matrix equation (3.25) but once the all-pole
coefficients amk have been estimated, each method generates the power spectrum PˆMEM ( f )
according to equation (3.24).
Burg’s algorithm
The autocorrelation matrix R x , x in equation (3.25) has a Toeplitz structure, and the LevinsonDurbin recursion (Levinson, 1947a; Durbin, 1960) can be used to solve this equation. The direct
solution to equation (3.25), often referred to as the Yule-Walker method (Yule, 1927; Walker,
1931), uses traditional sample correlations to estimate the autocorrelation values rx , x ( k ) .
Equation (3.25) of the maximum entropy method assumes however that the autocorrelation lags
rx , x ( k ) are precisely known, but windowing end-effects are unavoidable when the
autocorrelation lags are directly evaluated from the data. In order to avoid these end-effects and
keep the potential resolution of MEM, Burg developed an algorithm to evaluate the coefficients
amk that does not use the estimated autocorrelation lags rx , x ( k ) as input. The basis of the
algorithm is that the first (N+1) lags of the autocorrelation can be estimated by evaluating the
corresponding (N+1)-point prediction error filter. Burg’s recursive algorithm (Burg, 1968 and
1975; Andersen, 1974) is based on minimizing the average (forward and backward) prediction
error filter output power, starting from a model order equal to 0 and stepwise (Levinson’s
recursion) increasing the matrix dimension in equation (3.25) until the last coefficient amm for a
40
Frequency (Hz)
5
10
15
20
25
30
35
40
45
50
V (t ) = 10sin(2π 20.5t )
0
5
10
15
20
25
30
35
40
45
103
102
101
100
10-1
10-2
10-3
10-4
10-5
10-6
10-7
10-8
PSD (volt2/ Hz)
2
PSD (volt / Hz)
0
103
102
101
100
10-1
10-2
10-3
10-4
10-5
10-6
10-7
10-8
50
Frequency (Hz)
Figure 3.4 One-sided Maximum Entropy Method (Burg’s algorithm) PSD of a 20.5 Hz harmonic potential
difference V(t) of 10 volts peak amplitude. 256-point data segment, 0.010 sec sampling period, AR order = 2, 10,000
frequencies. The periodogram is shown in gray for comparison.
chosen order M is computed. It is important to note that with Burg’s algorithm, the prediction
error filter never runs off the ends of the data sample. The usual assumptions about the time
series like zeros before and after the data sample, or periodicity of the data segment, are thus not
made. Instead, Burg’s algorithm makes an implicit prediction of the signal beyond the
observation window.
Figure 3.4 displays the Maximum Entropy Method PSD of the example signal, computed with
function “pburg” (Burg’s algorithm) of Matlab Signal Processing Toolbox. The AR model order
M is 2 and the spectrum is evaluated at 10,000 frequencies. For signals composed of very sharp
spectral features as in this example, MEM usually requires a higher number of frequencies than
classical methods do because a great deal of the power can be concentrated in only a few very
closely spaced frequencies. Contrary to classical methods, MEM does not perform zero padding
when the desired number of frequencies exceeds the number of data points. In Figure 3.4, the
peak is so sharp that there is no sample close to the 10 percent level on both sides of the peak,
even when 10,000 frequencies are used. With this number of frequencies, the 20.5 Hz peak is
only 0.02 Hz wide at the 0.1 percent level of the peak value. The main properties of this MEM
spectrum are thus high sharpness of the peak, and low, smooth leakage.
41
Selection of the model order in MEM
The duality between MEM and the fitting of an autoregressive model has allowed to apply
results from the AR literature to the maximum entropy method. In particular, objective criteria to
the selection of the order M in autoregressive models have significantly contributed to MEM. If
the model order is too small, the resulting spectrum will be too smooth and will have poor
resolution. On the other hand, if the model order is too large, then the spectrum may contain
spurious peaks and spectral line splitting may result.
Akaike’s Final Prediction Error (Akaike, 1969) chooses the order of the autoregressive model by
minimizing the average error power for a one step prediction, considering both the error power
due to the unpredictable part of the process (the innovation) and the error power due to
inaccuracies in estimating the AR coefficients. With the mean of the data sample removed, the
FPE is given by
FPE( M ) = ε M
N + M +1
.
N − M −1
(3.27)
In FPE, N is the number of points of the observed data segment, M is the AR model order and
ε M is the modeling error power for order M. Akaike’s An Information theoretic Criterion
(Akaike, 1974) is an extension of this model selection to any maximum likelihood situation. For
an AR process with Gaussian errors, and data sample mean removed, the AIC is
AIC( M ) = N ln ε M + 2(1 + M ) .
(3.28)
In both methods, the optimal order M 0 is the model order that minimizes the selected criterion
(FPE or AIC). AIC and FPE are asymptotically equivalent and nearly always select the same
optimal order M 0 (Jones, 1974).
Jones (1976) has further shown that the FPE criterion, developed originally for the Yule-Walker
method of solving equation (3.25), applies also to Burg’s algorithm as long as the model order M
is not greater than N / 2 . For higher orders, the FPE criterion provides overestimated M 0 values.
This is especially important when Burg’s algorithm is used (Ulrych and Bishop, 1975) since the
variance of the results increases rapidly with this algorithm when the order of the model is
overestimated. Jones (1976) has well proposed an empirical correction to FPE for Burg’s
algorithm when N / 2 < M < N − 1 , but the practice however is generally to avoid model orders
greater than N / 2 .
42
Finally, Landers and Lacoss (1977) have shown that FPE or AIC criteria provide acceptable
spectra for harmonic processes with low levels of white noise. For higher noise levels (50%),
these criteria gave inconsistent and underestimated model orders. The authors conclude that in
general, FPE and AIC should be best seen as approximate indicators of the model order and not
as absolute criteria applicable in all cases.
Properties of an MEM spectrum
Because of the high degree of nonlinearity of MEM, its properties are significantly more difficult
to ascertain than for classical methods. A full account of the known properties can be found in
Wu, 1997. The maximum entropy method has three main properties that make it an important
method for the design of an effective Wiener filter. I assume that MEM is implemented
according to Burg’s algorithm. The first property is that MEM tends to produce sharper spectral
features than classical methods do. This is a desirable property since the Wiener filter can then
be more tightly shaped around true spectral features. The second property of MEM is the
smoothness of spectra and low leakage since no widowing function is applied to the data. This is
also an important property since smooth spectra and low leakage are less likely to introduce
artifacts than spectra affected by numerous sidelobes. Finally, the most important property is that
MEM spectra for short data segments tend to be significantly better than those derived from
classical methods. This is particularly important in our case since stationarity requirements of the
Wiener filter impose the use of short data segments for spectral estimation.
Figure 3.5 displays an example of power spectral densities derived from a synthetic noise
segment of short duration (2 seconds) using the briefly reviewed methods of previous sections.
Three narrow beams of noise have been synthesized, with central frequencies located at 0.75,
2.00 and 5.00 Hz. Each beam is made up of three pure sinusoids, the amplitude at each central
frequency being twice the amplitude at the two adjacent frequencies within each beam (Table
3.2). In order to make the example more realistic, I added a low level (variance of 4.0 × 10-10
volts) of white Gaussian noise (Figure 3.5b) representing random noise and measurement errors.
The resulting waveform (Figure 3.5a) is thus composed of a deterministic component of noise
and of a random component of noise. Since only the deterministic part of the noise creates sharp
spectral features, it can be seen as the “signal” from the perspective of spectral analysis. The
background random noise is then the “noise”. The signal-to-noise ratio in this example is equal
to 28 dB, a very high value. The power spectra have been computed in Matlab with the same
functions that were used in the example of a monochromatic signal. In the case of the MEM
43
Time (sec)
1.5
2.0
1e-3
5e-4
5e-4
0
0
-5e-4
-5e-4
(a)
-1e-3
-1e-3
0.0
V(t) (volt)
1.0
1e-4
5e-5
0
-5e-5
-1e-4
V(t) (volt)
0.5
0.5
1.0
1.5
2.0
1e-4
5e-5
0
-5e-5
-1e-4
(b)
0.0
0.5
1.0
1.5
V(t) (volt)
V(t) (volt)
0.0
1e-3
2.0
Time (sec)
Frequency (Hz)
1
10
10-4
10-4
10-4
10-5
10-5
10-5
10-6
10-6
10-6
10-7
10-7
10-7
10-8
10-8
10-8
10-9
10-9
10-9
10-10
10-10
10-10
10-11
10-11
10-11
10-12
10-13
(c)
1
0.1
PSD (volt 2 / Hz)
0.1
10
2
10-12
3
1
10-13
(d)
1
0.1
10
2
10-12
3
1
10-13
10
10-4
10-4
10-4
10-5
10-5
10-5
10-6
10-6
10-6
10-7
2 tapers
10-7
10-8
10-9
10-8
10-7
M = 20
10-8
M = 50
10-9
10-9
10-10
10-10
10-11
10-11
10-11
10-12
10-12
10-10
10-13
1 taper
(e)
0.1
1
2
3
10-13
1
10
(f)
0.1
Frequency (Hz)
1
PSD (volt 2 / Hz)
2
PSD (volt / Hz)
1
2
PSD (volt 2 / Hz)
Frequency (Hz)
0.1
10-12
3
10-13
1
10
Frequency (Hz)
Figure 3.5 One-sided power spectral densities from a synthetic noise segment of short duration. (a) The noise
segment, expressed in volts (white Gaussian noise added): 201-point segment, 0.010 sec sampling period. (b) White
Gaussian noise of 4.0 × 10-10 volts variance. (c) Periodogram PSD: 8,192-point FFT. (d) Blackman-Tukey PSD:
8,192-point FFT and 201-point Hamming window (its shape is in the upper-right corner). (e) Multitaper PSD: 8,192point FFT, 1 taper (black) and 2 tapers (dark gray). (f) Maximum entropy (Burg’s algorithm) PSD: 8,192
frequencies, AR orders 20 (dark gray) and 50 (black). The three beams of deterministic noise are displayed in gray
and labeled in white on the PSD plots.
44
spectrum, the optimal model order was determined according to the FPE criterion, the modeling
error ε M being a possible output of function “arburg” which computes the AR coefficients in the
Signal Processing Toolbox of Matlab.
Table 3.2 Parameters of the deterministic part of the noise in Figure 3.5
Beam
Peak Amplitude A
Frequency F
Phase φ
#
(volt)
(hertz)
(radian)
1
-4
2 × 10
0.675
0
1
4 × 10-4
0.750
0
1
-4
0.825
0
2
-5
5 × 10
1.800
- π / 16
2
1 × 10-4
2.000
- π / 16
2
-5
5 × 10
2.200
- π / 16
3
1 × 10-5
4.500
- π / 32
3
-5
2 × 10
5.000
- π / 32
3
1 × 10-5
5.500
- π / 32
2 × 10
Potential difference as a function of time is given by V ( t ) = A sin(2π Ft +φ ) .
Parameters of the central sinusoid of each beam are shaded in light
gray.
As expected, the periodogram (Figure 3.5c) has a poor resolution. Furthermore, strong sidelobes
from beam 1 interfere with beam 2, and combined sidelobes from beams 1 and 2 render the
detection of the weak beam 3 uncertain without the a priori knowledge of its existence. The
Blackman-Tukey spectrum (Figure 3.5d) is much smoother than the periodogram but the
resolution further degrades. Beam 3 has also lost too much amplitude to be easily detected
without a priori knowledge. With only one taper, beams 1 and 2 of the multitaper spectrum
(Figure 3.5e) are only slightly better defined than in the Blackman-Tukey spectrum. This is not
surprising since the multitaper method differs little from the Blackman-Tukey method when only
one taper is applied. Beam 3 suffers from severe interference with sidelobes of the two stronger
beams as in the case of the periodogram. With 2 tapers, the lack of resolution up to at least 3 Hz
is such that the single-taper spectrum appears to be far better. As a whole, classical methods
perform about equally poorly in this example. In particular, the multitaper method seems to have
lost most of its strengths on this short data segment. The maximum entropy spectrum (FPE
optimal order M 0 = 50 ) has however no problem (Figure 3.5f) in clearly resolving the three
beams. The weak beam 3 is particularly well defined compared to classical methods, both in
45
width and in amplitude. If the model order is severely underestimated as when an order 20 is
selected, a considerable smoothing is produced and beams 2 and 3 just disappear. In that case,
the peak value corresponding to beam 1 shifts also toward a slightly higher frequency. This
extreme case illustrates the importance of selecting an appropriate model order in MEM.
Marple (1982) has shown that for two complex sinusoids, the resolution of MEM is increasing
when the signal-to-noise ratio increases. When the SNR is very low (SNR ≈ –30 dB), the
resolution of MEM tends toward the resolution of the Blackman-Tukey method, which is
independent of the SNR. For a fairly high SNR, the resolution of MEM is however significantly
higher than the resolution obtained with the Blackman-Tukey method.
The asymptotical properties of MEM have been investigated by Kromer (1970). His findings
indicate that the MEM spectral estimate is asymptotically normal, and unbiased
{
}
lim E PˆMEM ( f ) = PX , X ( f ) .
N →∞
(3.29)
The variance of the MEM estimate is given for large N (number of data points) and M (AR
model order) by
{
}
2M 2
Var PˆMEM ( f ) =
PX , X ( f ) .
N
(3.30)
Asymptotically, the variance of the MEM estimate is approximately equivalent to that of the
Blackman-Tukey estimate with a suitably chosen truncation length (Gersch and Sharpe, 1973).
Despite the existence of asymptotical properties, MEM suffers from the lack of a clearly defined
variance in the important cases for which N and M are not large. Baggeroer (1976) has however
proposed a method of determining confidence intervals for Yule-Walker MEM spectral
estimates. When noise is added to the exact autocorrelation of a real sinusoid (Lacoss, 1971), the
MEM estimates display much larger variations in the peak value than Blackman-Tukey estimates
do. However, fluctuations of the area under the peak (the estimated power) are comparable to the
fluctuations in the peak value obtained with the Blackman-Tukey method. With two sinusoids,
MEM tends to suppress a lower peak relatively to a higher one. As a result, the ratio between the
high and low peak values is greater than their power ratio (square of the power ratio). This effect
is compensated by a broadening of the lower peak in such a way that the area under the peak (the
integrated power) reflects the true power of the lower peak. It is not clear however whether this
property of MEM remains valid or not in the case of continuous spectra. A method for obtaining
46
a power estimate without numerical integration has been presented by Johnson and Anderson
(1978).
Despite their particular qualities, MEM and related methods have never gained popularity in
seismology. This is probably related to the immense popularity of Fourier methods as a result of
the existence of highly versatile FFT algorithms. The model order determination in MEM might
also have been an obstacle to its more widespread use. MEM and autoregressive methods appear
however to be highly relevant to several aspects of the analysis of seismograms. Various
seismological applications are documented, ranging from characterization of seismograms and
high-quality power spectrum estimation (Lacoss, 1971; Leonard and Kennett, 1999) to automatic
onset picking methods of single-component and multi-component recordings as mentioned
earlier (Morita and Hamaguchi, 1984; Takanami and Kitagawa, 1988; Kushnir et al., 1990;
GSE/Japan/40, 1992; Leonard and Kennett, 1999; Sleeman and van Eck, 1999; Takanami and
Kitagawa, 2003). Phase onset picking is probably the most important application of
autoregressive methods in seismology today.
Power spectrum estimation in MannekenPix
Since MEM appears to have the important and rare qualities required for the design of an
effective Wiener filter derived from short data segments, I selected this method to evaluate
power spectra in MannekenPix. Among the various algorithms available, MannekenPix uses the
classical Burg’s algorithm implemented in the “Numerical Recipes in Fortran” (Press et al.,
1992). The validity of this particular implementation is supported by an atmospheric angular
momentum study (Penland et al., 1991), and results derived from the Numerical Recipes closely
match also those obtained with the Signal Processing Toolbox of Matlab 6.0.
Routine “Memcof” evaluates the AR coefficients, and routine “Evlmem” evaluates the power
spectral density at a given frequency. Once the AR coefficients have been determined for a given
model order, successive calls to “Evlmem” allow to form a complete spectrum, one frequency
per call.
Three methods of determining the optimal model order have been tested. In the first method,
fixed orders were used, the optimal order being the model order maximizing a criterion that takes
into account both the accuracy and the hit rate (the relative frequency of picked seismograms) of
the picking for a whole data set. In the second method, Akaike’s FPE criterion was used to select
47
an optimal model order for each seismogram. In the third method, the optimal model order was
the order maximizing the signal-to-noise ratio after the application of several Wiener filters with
different model orders for each seismogram.
A data set composed of more than 1,000 short-period seismograms from local earthquakes
recorded by stations located in the vicinity of the Dead Sea basin, was carefully re-picked and reweighted manually (see Chapter 4). The automatic picking of this reference set with
MannekenPix revealed only a weak sensitivity of the global results to the model order for orders
not greater than half the sample size. The third method, i.e. a model order derived from the
optimal signal-to-noise ratio, appeared however to provide the best global results and was
adopted as the standard method to select the model order in MannekenPix.
Application of the Wiener filter
Once the power spectrum of a segment of noise has been evaluated by MEM, it can be subtracted
from the power spectrum of a data segment containing both noise and signal in the vicinity of the
first-arrival time. The result is an approximation of the power spectrum of the P-wavetrain. The
magnitude spectrum of the Wiener filter can then be computed by equation (3.15).
In order to avoid introducing an additional delay to the onsets by the application of a causal
filter, MannekenPix uses a zero-phase finite impulse response (FIR) Wiener filter. FIR filters are
perfectly suited for implementing the complex shapes of Wiener filters because their magnitude
spectra can take nearly any shape, and their phase spectra can be made exactly linear or zerophase (e.g. Oppenheim et al., 1999). In addition, FIR filters are always stable.
Since the Wiener filter only attenuates frequencies for which the amount of signal is low
compared to the amount of noise, precursory signal sidelobes are usually not a concern with this
noncausal filter, and the signal amplitude remains quasi-unaffected by the filtering process.
Precursory noise sidelobes should well be produced but they contribute to the residual noise after
filtering, and they do not have the special importance that signal sidelobes have within the
framework of onset picking.
The Wiener filter is applied in MannekenPix by routine “convlv” (Press et al., 1992). This
routine multiplies the FFT spectrum of the data by the FFT spectrum of the Wiener filter but it
48
requires the inputs to be defined in the time domain. Since the Wiener filter of MannekenPix is
defined in the frequency domain, its impulse response is obtained by an inverse FFT.
The window techniques used to reduce the spectral leakage of power spectra can also be applied
to the impulse response of the Wiener filter in order to achieve higher stopband attenuations.
However, when narrow spectral features (a few 0.1 Hz wide) have to be canceled, the smoothing
introduced by windowing reduces the attenuation instead of improving it. Hamming and
Blackman windows have been tested but these windows did improve neither the accuracy nor the
hit rate of the picking. Consequently, MannekenPix does not window the impulse response of the
Wiener filter prior to its application.
Wiener filter and deconvolution applied to a synthetic example
In order to better understand how the various parts of the Wiener filter operate together in
MannekenPix, I designed a synthetic example where real-world seismic noise is combined with a
synthetic (P-wave) pseudo-wavetrain. Full details of how the example was build are provided in
Appendix B. The idea however is not to produce a completely realistic simulation of a seismic
record. I mainly want to show the typical distortion that a common recording system inflicts on
whatever it records, and how a Wiener filter and deconvolution can partially restore the original
signal. This process is quite general and it is as important to manual picking as it is important to
automatic picking.
First, I generated a synthetic source function (Figure B.1a in Appendix B) according to Brune’s
model (Brune, 1970) with program Pitsa (Scherbaum and Johnson, 1992). The Brune’s model
generates an S-wave source function but the distinction is not important here since P- and Ssource functions are not very different from each other. By convolving the source velocity
function (Figure B.1b) with a series of spikes of decreasing amplitude (Figure B.1c), a noiseless
pseudo-wavetrain of 3 seconds (Figure B.2a) length was produced.
Second, I extracted 10 seconds of noise from a seismogram of a local earthquake recorded in the
Dead Sea region by a short-period seismograph of GII. In order to better approximate true
ground noise, the recorded noise was deconvolved (Figure B.2b) by the response of a digital
seismograph (Figure B.5) composed of a simulated digital Marks L4-C seismometer (Figure B.3)
and a digital 5th-order Butterworth low-pass (anti-aliasing) filter (Figure B.4).
49
The pseudo-wavetrain was added to the background noise at time t = 7.0 sec (Figure B.2c). The
resulting time series simulates 7 seconds of pre-arrival noise and the first 3 seconds of a very
noisy P-wavetrain unaffected by the instrumental response. The filtering effect of the
seismograph (seismometer and anti-aliasing filter) is the final step and results in the simulated
recorded seismogram of Figure 3.6a. The first lobes of the pseudo-wavetrain are close to what
first-arrivals look like on real-world seismograms. What comes later is however not realistic
since it is not based on the propagation effects of waves through a layered medium. It is only
made of slowly decaying echoes of the source function. This is why I call it a pseudo-wavetrain.
Figure 3.6a displays the simulated recorded seismogram, where the noise segment and the
signal-and-noise segment used by the Wiener filter have been color-coded in red and purple
respectively. These two segments are 2.0 seconds long each, and they are separated from each
other by a double safety gap of 100 msec (Figure 3.6c) around the true arrival time t = 7.0 sec.
The very high level of noise makes it impossible to accurately pick the onset time or even to
confidently identify the polarity of first-arrival motion.
The power spectra of the unfiltered seismogram (Figure 3.7a) show that the power density of the
noise is concentrated around 1.7 Hz while the power density of the estimated signal is
concentrated around 10.0 Hz. The high level of the estimated signal between 0.1 and 1.2 Hz
appears dubious, and results at least partially from an imperfect stationarity of the noise between
the noise segment and the signal-and-noise segment. In addition, the very high level of noise
adversely affects the accuracy of the estimation of the signal power spectrum.
The shape of the Wiener filter (Figure 3.7b) is however rather simple and consists mainly of
three narrow rejection bands, among which the band centered at 1.7 Hz is the most important one
since it largely contains most of the noise power. The plot also displays the magnitude spectrum
of the un-windowed FIR filter truncated in the time domain to a length of 4 seconds, and the
spectrum of the corresponding Hamming-windowed filter. The rejection band centered at 1.7 Hz
is too narrow to benefit from windowing and the un-windowed filter provides a better attenuation
of the noise in this narrow band. The windowed filter appears however to perform better in the
two broader rejection bands, but the contribution of these bands to the total noise is minor
compared to the low-frequency band. As a whole, the un-windowed filter appears thus to
perform better.
50
Time (sec)
2
3
4
5
6
7
8
9
10
500
400
400
300
N
300
SN
200
200
100
100
0
0
-100
-100
-200
-200
-300
500
-300
500
400
400
300
300
200
200
100
100
0
0
-100
-100
-200
-200
-300
-300
0
1
2
3
4
5
6
7
8
9
(a)
Voltage (µV)
1
(b)
Voltage (µV)
Voltage (µV)
Voltage (µV)
0
500
10
Time (sec)
Voltage (µV)
(c)
7.0
6.5
7.0
500
400
400
300
300
200
N
200
SN
100
100
0
0
-100
-100
-200
-200
-300
-300
-400
-400
6.5
7.0
6.5
Time (sec)
(d)
Voltage (µV)
6.5
500
7.0
Time (sec)
Figure 3.6 Simulated seismogram of a synthetic P-wave pseudo-wavetrain as it would be recorded by a shortperiod seismograph. (a) Raw seismogram (full). (b) Wiener-filtered seismogram (full). (c) Raw seismogram (detail).
(d) Wiener-filtered seismogram (detail). The first arrival occurs at time t = 7.0 sec and is marked by the dark red
vertical line. The 2-seconds noise (N) segment used in the evaluation of the Wiener filter is plotted in red (a,c). The
2-seconds signal-and-noise (SN) segment used in the evaluation of the Wiener filter is plotted in purple (a,c). The
sampling period is 10 msec.
51
Frequency (Hz)
10
1e-9
1e-10
1e-10
1e-11
1e-11
1e-12
1e-12
1e-13
1e-13
1e-14
1e-14
1e-15
1e-15
Magnitude
1
1
0.1
0.1
0.01
0.01
0.001
0.001
0.78Hz
PSD (volt2/Hz)
0.0001
1e-8
0.93Hz
1.76Hz
0.0001
1e-8
1e-9
1e-9
1e-10
1e-10
1e-11
1e-11
1e-12
1e-12
1e-13
1e-13
1e-14
1e-14
1e-15
1e-15
0.1
1
2
1e-9
(a)
PSD (volt /Hz)
1e-8
(b)
Magnitude
1e-8
(c)
2
1
PSD (volt /Hz)
PSD (volt2/Hz)
0.1
10
Frequency (Hz)
Figure 3.7 Power spectra and Wiener filter of the simulated seismograms plotted in Figure 3.6. (a) Power spectra
before Wiener filtering (Noise in red, mixed Signal-and-Noise in purple, and estimated Signal in blue). (b) Wiener
filter magnitude spectrum derived from power spectra plotted in (a). Ideal Wiener filter in green, actual filter (unwindowed FIR of 4 sec.) as solid black, and windowed (Hamming) filter as dashed black. The 3 values at the bottom
indicate the width (in Hz) of the narrow bands where a total cancellation of the noise is expected. (c) Power spectra
of the Wiener-filtered seismogram. A MEM model order value of 9 has been selected, maximizing the signal-tonoise ratio of the Wiener-filtered seismogram.
52
The power spectra of the filtered seismogram (Figure 3.7c) reveal the presence of low-frequency
(below 0.5 Hz) residual noise, easily observable on the seismogram (Figure 3.6b). This lowfrequency noise has however very little incidence on the picking because its amplitude is now
moderate compared to the amplitude of the signal, and the frequencies of the signal are much
higher and quite distinct from those of the noise. One possible way to further reduce the residual
noise would be to apply an additional Wiener filter to the already filtered seismogram. Such a
procedure might prove beneficial to this particular example but it appears to degrade results
when it is systematically used on large data sets.
The Wiener-filtered seismogram allows a far better identification of the first-arrival motion
polarity (Figure 3.6b and d), and the uncertainty on the onset time is about ± 30 msec at the most
(Figure 3.8a). A comparison between the noiseless recorded signal and the filtered seismogram
(Figure 3.8a) demonstrates also that the Wiener filter does not delay the recorded signal. Due to
residual noise, the example is however not conclusive about the absence of precursory sidelobes.
In order to partially correct the delay and distortion (Figure B.6) of the signal created by the
seismograph, the Wiener-filtered seismogram was further deconvolved by the impulse response
(Figure B.5) of the seismograph. The deconvolution was performed by spectral division in
Matlab (see Appendix B), regularized by a small water-level value of 5 × 10-10.
The result is plotted in Figure 3.8b along with the true signal, and it clearly demonstrates the
potential importance of deconvolution for picking purposes. The most beneficial effect of
deconvolution is perhaps its ability to re-focus the signal, smeared in this example by the awful
phase properties of the Butterworth anti-aliasing filter. It is almost impossible to correctly
identify the main features of the true signal from the Wiener-filtered seismogram (Figure 3.8a)
alone. The filtered and deconvolved seismogram (Figure 3.8b) is also far from being perfect due
to the residual noise but it accurately depicts several features of the true signal. For instance, the
impulsive rise of the first arrival and echoes is rather well recovered and the sharp tips coincide
exactly with those of the true signal. The first arrival and echoes displayed in Figure 3.8b are a
bit broader than the true signal but they are clearly resolved, and they are also much closer to the
true signal than on the Wiener-filtered seismogram that was not deconvolved (Figure 3.8a). The
first-arrival onset time is also much easier to pick confidently. I would pick it at time t = 6.990
sec on the filtered and deconvolved seismogram, only one sample earlier than the true onset
time.
53
Time (sec)
6.8
6.9
7.0
7.1
7.2
7.3
7.4
7.5
7.6
200
200
150
150
100
100
50
50
0
0
-50
-50
-100
-100
-150
-150
-200
200
-200
200
150
150
100
100
50
50
0
0
-50
-50
-100
-100
-150
-150
-200
-200
-250
-250
-300
-300
-350
-350
-400
-400
-450
-450
-500
(a)
Voltage (µV)
6.7
(b)
Velocity (µm/sec)
Velocity (µm/sec)
Voltage (µV)
6.6
-500
6.6
6.7
6.8
6.9
7.0
7.1
7.2
7.3
7.4
7.5
7.6
Time (sec)
Figure 3.8 Deconvolution of the simulated seismogram by the seismograph response. (a) Wiener-filtered
seismogram (black), and noiseless signal filtered (gray) by the seismograph response (Figure B.5a). (b) Wienerfiltered seismogram deconvolved (black) by the seismograph response, and noiseless true signal (gray). The
sampling period is 10 msec.
3.3.2 AUTOMATIC PICKING
After the application of a Wiener filter in step 1 of MannekenPix, the automatic determination of
the first P-wave onset time is done by the picking algorithm of Baer and Kradolfer (1987).
This algorithm defines first an approximate squared envelope function Ei2 of the seismogram xi ,
given by
54
i
Ei2 = xi2 + x&i2
∑x
2
j
∑ x&
2
j
j =1
i
j =1
(3.31)
where x& denotes the time derivative of x. The algorithm uses then a characteristic function CFi,
defined as
CFi =
Ei4 − Ei4
σ 2 ( Ei4 )
(3.32)
in which Ei4 is the mean of Ei4 from j = 1 to i and σ 2 ( Ei4 ) is the variance of Ei4 . This
characteristic function differs only from the statistical Z score of Ei4 by the use of the variance
σ 2 as denominator in (3.32) instead of the standard deviation σ used in the Z score.
A pick flag is set if CFi increases above a given value Threshold1. The onset is accepted as a
valid pick only if the value of the characteristic function stays above Threshold1 for a certain
amount of time TUpEvent. If the characteristic function drops below Threshold1 after a shorter
duration than TUpEvent, the pick is rejected and the pick flag is removed. The pick flag is
however not removed if the characteristic function drops below Threshold1 for an amount of
time shorter than TdownMax. This happens frequently for events with low to moderate signal-tonoise ratios. The variance σ 2 ( Ei4 ) is continuously updated to account for variations of the noise
level, except when CFi exceeds the given value Threshold2 usually chosen greater than
Threshold1. The variance of Ei4 is thus frozen when the validity of the onset is examined, shortly
after the pick flag has been set.
In MannekenPix, the Threshold1 value of the characteristic function that triggers the pick flag is
determined in a fully adaptive and automatic way. For each seismogram, Threshold1 is first set
equal to the highest value of CFi within the time window corresponding to the noise segment of
the Wiener filter (e.g. Figure 3.6a). If the signal-to-noise ratio after the application of the Wiener
filter is greater than 14 dB, the value of Threshold1 is increased according to an internal table
derived empirically. Regarding the amount of time TUpEvent required to validate an onset after a
pick flag has been set, Baer and Kradolfer (1987) recommend to use at least one full cycle of the
longest signal period expected. In the case of local events that occured in the vicinity of the Dead
Sea basin, TupEvent has an optimal value at 0.5 sec. A value of 1.0 sec could be a sensible
choice when regional and local events are mixed together in one single picking set. The amount
of time TdownMax during which CFi can drop below Threshold1 without clearing the pick flag
has an optimal value in MannekenPix at half the signal period of highest power density as
55
measured by the Wiener filter routine. This value is quite consistent with Baer and Kradolfer
(1987) who recommend half the mean of the two corner periods of their bandpass filter.
Threshold2, the threshold value for freezing the variance update of Ei4 , is optimal in
MannekenPix at a value of 2 × Threshold1. This value is again in perfect agreement with the
recommendations of Baer and Kradolfer. Another good value for the Dead Sea data is 1.1 ×
Threshold1, but a value of 2 × Threshold1 minimizes the variance of the automatic picking
errors as determined from more than 1,000 reference picks.
Figure 3.9 displays the automatic picking result of the Wiener-filtered synthetic example of
section 3.3.1. The plot was exported from program Visual Picker 1.2, in which most functions of
MannekenPix are implemented with a graphical interface. MannekenPix was unable to find a
valid onset for this example. The characteristic function triggers well the pick flag at time t =
7.040 sec but it does not stay long enough above the Threshold1 value to validate the pick.
3.3.3 DELAY CORRECTIONS
One known shortcoming (e.g. Sleeman and van Eck, 1999) of the Baer-Kradolfer algorithm is
that the raw picking time provided is always somewhat late compared to what an analyst would
determine as the onset time of a valid phase. For local earthquake data recorded by short-period
instruments, this delay can be as small as one sample for the best seismograms. An example of
such a small delay is provided in Figure 3.10b. For most seismograms, the delay is greater due to
the interference of noise. Figure 3.11d displays a noisy seismogram where a longer delay is
observed.
In order to reduce the delay of the Baer-Kradolfer onset times, all versions of MannekenPix
include a primary delay correction. This correction derives from how the onset is determined by
the Baer-Kradolfer algorithm. When a pick flag is set and validated, the characteristic function
value is generally far above the background level observed in the segment of noise immediately
preceding the onset. The idea for the correction is to move the raw automatic onset back in time
as long as the characteristic function decreases significantly toward earlier samples. The delay
correction stops when (CFi − CFi −1 ) is smaller than 0.01, or when this condition cannot be met
after moving back the onset by 3 samples. This process is not perfect since the characteristic
function may not decrease monotonically toward its background level, or because a clear
background level may not even exist in the vicinity of the onset due to the
56
CF
100
(a)
50
0
3 .5 0 0
3 .0 0 0
2 .5 0 0
2 .0 0 0
Amplitude (V)
1 .5 0 0
(b)
1 .0 0 0
0 .5 0 0
0 .0 0 0
- 0 .5 0 0
- 1 .0 0 0
- 1 .5 0 0
- 2 .0 0 0
6 .2 0 0
6 .3 0 0
6 .4 0 0
6 .5 0 0
6 .6 0 0
6 .7 0 0
6 .8 0 0
6 .9 0 0
T im e ( s e c )
7 .0 0 0
7 .1 0 0
7 .2 0 0
7 .3 0 0
7 .4 0 0
CF
Figure 3.9 Automatic picking of the Wiener-filtered synthetic example (Figure 3.6b). (a) Characteristic function
(CF). Lower dashed line is Threshold1, upper dashed line is Threshold2. (b) Wiener-filtered seismogram. Noise
segment in red, Signal-and-Noise segment in blue. True arrival time in dark blue at time t = 7.0 sec. CF does not
stay long enough above Threshold1 to validate the pick flag triggered at time t = 7.040 sec.
80
60
40
20
0
(a)
2 .0 0 0
1 .5 0 0
1 .0 0 0
Amplitude (V)
0 .5 0 0
0 .0 0 0
(b)
- 0 .5 0 0
- 1 .0 0 0
- 1 .5 0 0
- 2 .0 0 0
- 2 .5 0 0
- 3 .0 0 0
8 .1 5 0
8 .2 0 0
8 .2 5 0
8 .3 0 0
T im e ( s e c )
8 .3 5 0
8 .4 0 0
8 .4 5 0
8 .5 0 0
2 .0 0 0
1 .5 0 0
1 .0 0 0
Amplitude (V)
0 .5 0 0
0 .0 0 0
- 0 .5 0 0
(c)
- 1 .0 0 0
- 1 .5 0 0
- 2 .0 0 0
- 2 .5 0 0
- 3 .0 0 0
8 .1 5 0
8 .2 0 0
8 .2 5 0
8 .3 0 0
T im e ( s e c )
8 .3 5 0
8 .4 0 0
8 .4 5 0
8 .5 0 0
Figure 3.10 Automatic picking and delay correction of a high-quality seismogram from a local microearthquake
that occurred at the Northern end of the Dead Sea basin (recorded by GII, Date 04 Dec 1986, Sta MOI, Vertical
component short-period, O.T. 22:38:27.970, Dist 20.1 km, Depth 17 km, ML 2.0, Sampling 10 msec). (a)
Characteristic Function. Lower dashed line is Threshold1, upper dashed line is Threshold2. (b) Raw automatic pick
(cyan), and routine pick (dark blue). (c) Delay corrected automatic pick (cyan), and routine pick (dark blue). (b,c)
Noise segment in red, Signal-and-Noise segment in blue.
57
p
p
p
g
0 . 1 0 0
0 . 0 8 0
0 . 0 6 0
0 . 0 4 0
0 . 0 2 0
Amplitude (V)
0 . 0 0 0
- 0 . 0 2 0
(a)
- 0 . 0 4 0
- 0 . 0 6 0
- 0 . 0 8 0
- 0 . 1 0 0
- 0 . 1 2 0
- 0 . 1 4 0
- 0 . 1 6 0
- 0 . 1 8 0
- 0 . 2 0 0
1 2 . 0 0 0
1 3 . 0 0 0
1 4 . 0 0 0
1 5 . 0 0 0
p
T
1 6 . 0 0 0
im e
( s e c )
1 7 . 0 0 0
p
1 8 . 0 0 0
p
1 9 . 0 0 0
g
2 0 . 0 0
0 . 1 0 0
0 . 0 8 0
0 . 0 6 0
0 . 0 4 0
0 . 0 2 0
Amplitude (V)
0 . 0 0 0
- 0 . 0 2 0
(b)
- 0 . 0 4 0
- 0 . 0 6 0
- 0 . 0 8 0
- 0 . 1 0 0
- 0 . 1 2 0
- 0 . 1 4 0
- 0 . 1 6 0
- 0 . 1 8 0
- 0 . 2 0 0
1 2 . 0 0 0
1 3 . 0 0 0
1 4 . 0 0 0
1 5 . 0 0 0
CF
T
1 6 . 0 0 0
im e
( s e c )
1 7 . 0 0 0
1 8 . 0 0 0
1 9 . 0 0 0
2 0 . 0 0
20
10
0
-10
(c)
0.060
0.050
0.040
0.030
0.020
Amplitude (V)
0.010
0.000
-0.010
(d)
-0.020
-0.030
-0.040
-0.050
-0.060
-0.070
-0.080
-0.090
-0.100
15.400
15.500
15.600
15.700
15.800
15.900
T ime (sec)
16.000
16.100
16.200
16.300
0.060
0.050
0.040
0.030
0.020
Amplitude (V)
0.010
0.000
-0.010
(e)
-0.020
-0.030
-0.040
-0.050
-0.060
-0.070
-0.080
-0.090
-0.100
15.400
15.500
15.600
15.700
15.800
15.900
T ime (sec)
16.000
16.100
16.200
16.300
Figure 3.11 Automatic picking and delay correction of a noisy seismogram from a local microearthquake that
occurred in the Northern part of the Dead Sea lake (recorded by GII, Date 11 Nov 1986, Sta DSD2, Vertical
component short-period, O.T. 02:31:08.069, Dist 55.2 km, Depth 14 km, ML 1.6, Sampling 10 msec). (a) Unfiltered
seismogram. (b) Wiener-filtered seismogram. (c) Characteristic Function of (d,e). (d,e) Wiener-filtered seismogram
(detail of b). (d) Raw automatic pick (cyan), and routine pick (dark blue). (e) Delay corrected automatic pick (cyan),
and routine pick (dark blue). (a,b,d,e) Noise segment in red, Signal-and-Noise segment in blue.
58
disturbance by strong noise. Nevertheless, this simple correction usually provides good to very
acceptable results for local earthquakes recorded by short-period instruments. Figure 3.10c and
Figure 3.11e display the delay corrected onset times for the two examples presented before.
When regional and teleseismic data are picked with the original Baer-Kradolfer algorithm, raw
picking delays can be much longer than a few samples. This behavior of the algorithm has also
been observed by Sleeman and van Eck (1999). It results apparently from the fact that little or no
frequency contrast ( x& 2 terms in 3.31) between the P-wavetrain and the noise contributes then to
the build-up of the characteristic function for these events. At lower frequencies typical of
greater epicentral distances, the characteristic function is slow to reach the picking threshold
level. The primary correction becomes then insufficient.
CF
20
(a)
10
Amplitude (V)
0 .2 0 0
0 .1 8 0
0 .1 6 0
0 .1 4 0
0 .1 2 0
0 .1 0 0
0 .0 8 0
0 .0 6 0
0 .0 4 0
0 .0 2 0
0 .0 0 0
- 0 .0 2 0
- 0 .0 4 0
- 0 .0 6 0
- 0 .0 8 0
- 0 .1 0 0
- 0 .1 2 0
- 0 .1 4 0
- 0 .1 6 0
- 0 .1 8 0
- 0 .2 0 0
Amplitude (V)
0
0 .2 0 0
0 .1 8 0
0 .1 6 0
0 .1 4 0
0 .1 2 0
0 .1 0 0
0 .0 8 0
0 .0 6 0
0 .0 4 0
0 .0 2 0
0 .0 0 0
- 0 .0 2 0
- 0 .0 4 0
- 0 .0 6 0
- 0 .0 8 0
- 0 .1 0 0
- 0 .1 2 0
- 0 .1 4 0
- 0 .1 6 0
- 0 .1 8 0
- 0 .2 0 0
(b)
6 1 .0 0 0
6 1 .5 0 0
6 2 .0 0 0
T im e ( s e c )
6 2 .5 0 0
6 3 .0 0 0
(c)
6 1 .0 0 0
6 1 .5 0 0
6 2 .0 0 0
T im e ( s e c )
6 2 .5 0 0
6 3 .0 0 0
Figure 3.12 Automatic picking and deviation band delay correction of a seismogram from a regional earthquake
that occurred in Turkey ~ 60 km N-W of Ankara (Recorded in Italy by INGV, Date 23 Aug 2000, Sta EB9 ~ 80 km
W of Bologna, Vertical component short-period, O.T. 13:41:12.400, Dist 1,850 km, Depth 10 km, M 5.0, Sampling
20 msec). (a) Characteristic Function. Lower dashed line is Threshold1, upper dashed line is Threshold2. (b) Raw
automatic pick (cyan), and routine pick (dark blue). (c) Deviation band delay corrected automatic pick (cyan), and
routine pick (dark blue). (b,c) Noise segment in red, Signal-and-Noise segment in blue, and deviation band limits in
gray.
59
In order to better correct the delay for regional and teleseismic arrivals, I introduced a secondary
delay correction in version 1.7 of MannekenPix. This secondary correction is applied
immediately after the primary correction. It does not appear to interfere adversely with the
primary correction, so important for local earthquake data. An example of a first P-wave onset
from a regional earthquake is presented in Figure 3.12b (from Istituto Nazionale di Geofisica e
Vulcanologia, Roma). The earthquake occurred in Turkey near Ankara and was recorded near
Bologna in Italy at an epicentral distance of about 1,850 km. The routine pick appears to be quite
well located on the seismogram but the raw automatic onset time is late by about five samples.
Since the characteristic function is not monotonically decreasing toward its background level
when looking backward in time, the primary correction just applies an insufficient delay
correction of one sample to the raw automatic time.
For non-impulsive events where the picking is primarily the result of an amplitude anomaly, a
good delay correction is obtained by moving the pick earlier until a value of the seismogram
becomes located inside a moving standard deviation band. A simple moving average SMA i,P of
period P is given at the seismogram sample index i by
P −1
SMAi ,P =
∑x
i− j
j =0
P
, i ≥ P.
(3.33)
The corresponding simple moving standard deviation SMSTDi ,P is then
1/ 2
SMSTDi ,P
⎡ P −1
2⎤
⎢ ∑ ( xi − j − SMAi ,P ) ⎥
⎥
= ⎢ j =0
P
⎢
⎥
⎢
⎥
⎣
⎦
, i ≥ P.
(3.34)
MannekenPix 1.7 uses a number of samples P in (3.33) and (3.34) corresponding to the period
of highest noise spectral density as determined by the Wiener filter routine. The standard
deviation band of MannekenPix 1.7 is defined as
STDBi ,P = SMAi ,P ± 2 × SMSTDi ,P , i ≥ P.
(3.35)
For a positive onset (increasing amplitude of first motion), the precise condition is that the delay
correction stops at the first sample xi below the higher value of STDBi ,P in (3.35). This
condition is usually met at an intermediate value between the two STDBi ,P values. For a negative
onset, the delay correction stops at the first sample xi above the lower value of STDBi ,P . The
60
secondary correction is however skipped if the seismogram value xi at the onset time corrected
by the primary correction is not out the deviation band STDBi,P by more than 0.1 × SMSTDi,P.
The raw automatic picking time of the regional earthquake of Figure 3.12b has been corrected by
the primary and secondary delay corrections and the result is displayed in Figure 3.12c. The
agreement between the manual pick and the final automatic pick is now excellent on this
example.
3.3.4 WEIGHTING
In order to take into account the estimated uncertainty associated with picked phases, location
and tomographic programs usually expect pick times to be accompanied by quality labels. In
most applications, the highest quality is expressed by a small label value like 0 or 1 while the
poorest quality is expressed by a higher value like 3, 4 or 5. These quality labels are then
converted by the applications into observation weights that provide a variable importance to the
arrival times according to their reported quality.
Uncertainties on arrival times are intervals of time. However, since the input of picking
uncertainties into location and tomographic programs is not explicitly done as intervals of time, I
am not sure that quality labels always reflect time uncertainties in practice. The use of quality
labels instead of duration values appears to me as a choice favoring mispractices. It would have
been far more in agreement with standard practices of the physical sciences to require the
uncertainties to be expressed directly in seconds, or at the very least to require the quality labels
to have the precise quantitative meaning they are supposed to have.
The weighting mechanism of the Baer-Kradolfer (1987) algorithm implemented in Pitsa
(Scherbaum and Johnson, 1992) is based on the ratio between the P-wave amplitude within a
certain time window and the largest amplitude of the seismogram before the pick flag is set for
the first time. This kind of signal-to-noise ratio is certainly important for the weighting of arrival
times, but I think that any variable by itself cannot carry all the information necessary to properly
discriminate among time uncertainty groups. The weighting mechanism included in the Allen
(1978, 1982) picking system is a great quality of this older system, and it uses four or five
variables (depending on the implementation) to provide a pick weight. With a higher number of
variables, it is potentially more powerful than the weighting mechanism included in Pitsa. One
limitation of the Allen weighting mechanism is however that absolute thresholds (450 mV,
61
200mV, …) for the amplitude of the P-wave intervene in the classification process. This might
be a good choice for dense networks like the ones located in California, but it is certainly
introducing a pessimistic bias for sparser networks where less redundancy is available. A
common shortcoming of these two weighting mechanisms is that very little is known about the
relation between their quality labels and time uncertainties. The core of the problem is not the
internal consistency of these weighting mechanisms, it is how well the quality labels they
provide correlate with time uncertainties on the readings.
MannekenPix includes a weighting mechanism where picking uncertainties are expressed as
standard labels 1 to N, with N not greater than 5. A precise uncertainty duration defined by the
user is however associated with each of these labels. This weighting mechanism is based on the
discriminating power provided by the simultaneous use of several predicting variables as in the
Allen picking system. Adapting the weighting mechanism of the Allen system to particular
networks and data requires however a lot of trial-and-error at the very least. In MannekenPix, a
calibration is made according to a statistical technique known as discriminant analysis on
reference picks and associated weights supplied by the user. This calibration cannot be
performed internally by MannekenPix at the moment, but it can be easily performed from the
automatic picking output of the reference data set with a package like SAS, SPSS, or equivalent.
Discriminant analysis
Discriminant analysis is a statistical technique whose general purpose is to identify quantitative
relationships between two or more criterion groups and a set of discriminating variables also
called predictors. It requires the criterion groups to be mutually exclusive, and it assumes the
absence of collinearity among discriminating variables, the equality of population covariance
matrices and multivariate normality for each group. The mathematical objective is to weight and
linearly combine the predictors in a way that maximizes the differences between groups while
minimizing differences within groups (Fischer, 1936, 1938). When more than two groups are
involved, the technique is commonly referred to as multiple discriminant analysis (MDA). As a
descriptive technique, discriminant analysis serves to explain how various groups differ, what the
differences between and among groups are on a specific set of discriminating variables, and
which of these variables best account for the differences. As a predictive technique, it is used to
predict the unknown group membership of cases based on the actual value of the discriminating
variables.
62
The problem at hand in the weighting mechanism of MannekenPix is to predict the uncertainty
group of automatic pick times from quantitative variables evaluated by the program. In order to
be able to perform these predictions, it is however necessary to derive classification rules from
an initial descriptive discriminant analysis on data for which the group membership is known.
For a given data set, this discriminant analysis provides valuable guidelines to the user regarding
both the definition of appropriate uncertainty groups and the selection of the most relevant
predictors. The insight provided by the canonical discriminant functions also assists in the
development of the weighting mechanism of MannekenPix by helping with the selection of a
pool of standard predictors. The group membership predictions on unseen data are not done in a
statistical package. MannekenPix performs this prediction internally by computing Fischer’s
linear discriminant functions from the coefficients determined during the initial descriptive
discriminant analysis.
The discriminating variables of MannekenPix
The lack of discriminating power resulting from the use of only one predictor can be easily
understood. For instance, any signal-to-noise ratio (SNR) derived from a segment of signal and a
segment of noise implies already that a limiting choice has been made. Basically, the length of
the segments can be chosen to be long or short compared to the dominant period of the signal. If
long segments are selected, chances are that a general characterization of the overall quality of
the seismograms will be gained. This overall quality might then discriminate rather well between
picks located far away from true onsets and those located closer from true onsets. What is
missing however in the prediction process is a localized SNR value derived from very short
segments. Used in isolation, this localized SNR might reflect the accuracy of the picked features,
but little will be known about the possibility of gross errors. When the information provided by
both predictors is combined, some discriminating power is gained because a decision matrix can
then be derived with information about both the possibility of gross errors and a very localized
quality factor. Similarly, the discriminating power can be further increased by adding appropriate
variables in the prediction process. Naturally, defining the most appropriate predictors is not a
straightforward task.
The benefits of using discriminant analysis for this purpose are that trial-and-error is reduced to a
minimum, no decision matrix needs to be coded explicitly, and the best predictors for specific
data sets can be easily selected from the pool of standard discriminating variables already
gathered. Discriminant analysis is thus useful both to define new predictors, and to select the
63
available ones most appropriate to tackle specific data sets. The pool of standard predictors
available so far includes 9 variables evaluated internally by MannekenPix. On specific data sets,
the optimal number of predictors usually ranges from 6 to 8 among the 9 available.
Predictor 1 (WfStoN) is a signal-to-noise ratio derived from the signal and noise power spectra
determined by the Wiener filter routines. Its value is evaluated at the final automatic onset time
and it is given in decibels by
FNy
∑P
(f)
∑P
(f)
f =0
10 FNy
P1 = 10log
f =0
S ,S
(3.36)
N ,N
where PS ,S ( f ) and PN , N ( f ) are the power spectral densities of the signal and the noise
respectively, and FNy is the Nyquist Frequency. Although the Wiener filter uses short data
segments (about 2 sec for local data), the length of these segments is long compared to one
apparent cycle of the P-wavetrain. Predictor 1 is an overall quality estimate around the final
automatic onset time.
Predictor 2 (GdStoN) is a signal-to-noise ratio determined by the delay correction routines. Its
value is evaluated at the final automatic onset time and it is given in decibels by
FNy
P2 = 20log10
∑A (f)
f =0
FNy
S
∑A
f =0
N
(3.37)
(f)
where AS ( f ) and AN ( f ) are the magnitude spectra of the signal and the noise respectively, and
FNy is the Nyquist frequency. The length of the noise segment is half the length of the Wiener
filter noise segment. The signal segment extends from the picked onset until the second zerocrossing after the onset. Its length is about one apparent cycle of the P-wavetrain. Predictor 2 is a
localized measure of quality at the final automatic onset time.
Predictor 3 (GdAmpR) is a signal-to-noise ratio determined in the time domain by the delay
correction routines. Its value is evaluated at the final automatic onset time and it is given in
decibels by
P3 = 20log10
64
AmpS
AmpN
(3.38)
where AmpS and AmpN are the peak-to-peak maximum amplitude of the signal and noise
respectively. The length of the noise segment is half the length of the Wiener filter noise
segment. The signal segment extends from the picked onset until the second zero-crossing after
the onset. Its length is about one apparent cycle of the P-wavetrain. Predictor 3 is also a localized
measure of quality at the final automatic onset time.
Predictor 4 (GdSigFR) is the signal-to-noise ratio evaluated at the dominant frequency of the
signal, as determined by the delay correction routines. Its value is evaluated at the final
automatic onset time and it is given in decibels by
P4 = 20log10
AS ( FS )
AN ( FS )
(3.39)
where AS ( FS ) is the value of the magnitude spectrum of the signal at the dominant frequency of
the signal f = FS , and AN ( FS ) is the value of the magnitude spectrum of the noise at frequency
f = FS . The length of the noise segment is half the length of the Wiener filter noise segment.
The signal segment extends from the picked onset until the second zero-crossing after the onset.
Its length is about one apparent cycle of the P-wavetrain. Predictor 4 is also a localized measure
of quality at the final automatic onset time.
Predictor 5 (GdDelF) is the difference between the dominant frequency of the signal and the
dominant frequency of the noise, as determined by the delay correction routines. Its value is
evaluated at the final automatic onset time and it is given in hertzs by
P5 = FS − FN
(3.40)
where f = FS is the dominant frequency of the signal and f = FN is the dominant frequency of
the noise. The length of the noise segment is half the length of the Wiener filter noise segment.
The signal segment extends from the picked onset until the second zero-crossing after the onset.
Its length is about one apparent cycle of the P-wavetrain. Predictor 5 is a localized measure of
the frequency contrast between the signal and the noise.
Predictor 6 (ThrCFRat) is the natural logarithm of the ratio between the first maximum of the
characteristic function after picking to the Threshold1 value, as determined by the automatic
picking routines. It is given by
P6 = ln
CFMax1
Threshold 1
Predictor 6 is a localized measure of quality derived from the characteristic function.
65
(3.41)
Predictor 7 (PcAboThr) is the percentage of characteristic function samples above the
Threshold1 value before the picked onset, as determined by the automatic picking routines. The
data segment has the length of the Wiener filter noise segment and stops one sample before the
picked onset. A Predictor 7 value different from zero is often associated with a possible earlier
pick time, or with a high level of pre-arrival noise.
Predictor 8 (PcBelThr) is the percentage of characteristic function samples below the
Threshold1 value after the picked onset, as determined by the automatic picking routines. The
signal data segment length is 1/10 the length of the Wiener filter mixed signal-and-noise segment
and starts at the picked onset. A Predictor 8 value different from zero is often associated with
low to moderate signal-to-noise ratios.
Predictor 9 (CFNoiDev) is a measure of deviation of the characteristic function before the
picked onset, as determined by the automatic picking routines. It is given by
N
∑ CF − CF
i =1
P9 = ln
i
median
N
Threshold 1 − CFmedian
(3.42)
where the CFi are the N samples of the characteristic function in a noise segment of length equal
to the length of the Wiener filter noise segment, and CFmedian is the median value of CFi over the
N samples.
66
Chapter 4
High-quality automatic picking of local earthquake data
from the Dead Sea region
The automatic picking system MannekenPix was initially developed to collect a high-quality set
of picking data from local earthquakes that occurred in the vicinity of the Dead Sea basin. This
data set would then be used in another work to perform a high-resolution travel-time
tomographic study of the crustal structure of the region.
Figure 4.1 displays the set of 531 well-locatable (≥ 8 P Picks and Gaps < 180°) earthquakes
recorded by GII during the period 1984-2001 for which digital seismograms could be retrieved.
The yearly distribution of seismograms is shown in Figure 4.2. The data set is complete for the
period 1984-1996 but a final check is required for the period 1997-2001, and it does not include
any earthquake after September 2001. Eighty short-period stations (L4-C and some S-13)
operated by GII and 10 short-period stations operated by JSO carry first-arrival P-readings. The
coordinates of the 90 stations are provided in Appendix C. Most stations are vertical singlecomponent stations, and only the vertical component has been used for the few three-component
stations available. All the data were recorded by GII, mainly at a sampling rate of 50 Hz, but
some earthquakes were recorded at 100 Hz in 1986, 1987, and 1993.
All seismograms of a specific event are stored by GII in a single binary file. I wrote a program to
extract the seismograms from GII files and convert them to binary SAC format as required by
MannekenPix. The routine picking information has been written into the SAC headers from
related phase files. When no routine pick is available for a particular station, MannekenPix uses
the predicted arrival computed by the conversion program as the a priori time around which to
search for a P pick. The conversion program uses ray-tracing with model Israel (see 2.3) to
compute these predicted values.
67
Figure 4.1 Five hundred thirty-one well-locatable earthquakes (1984-2001) in the vicinity of the Dead Sea basin
recorded by short-period stations (triangles) of GII (Israel) and JSO (Jordan). The square grid fill defines the Dead
Sea basin, and the earthquake selection area is in yellow. DST: Dead Sea Transform. Topographic shaded relief
derived from Globe 1-km elevation data.
4.1 METHODOLOGY
The complete data set includes 15,250 seismograms, from which two subsets of particular
importance have been extracted (Figure 4.2). The first subset is the calibration set. It is used to
68
2500
2500
Complete Data Set
Seismograms: 15,250
Calibration Set
Reference Picks: 1,329
Validation Set
Reference Picks: 226
2000
2000
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
0
1989
500
1988
500
1987
1000
1986
1000
1985
1500
1984
1500
0
Figure 4.2 Yearly distribution of the number of seismograms and reference P picks.
determine the appropriate picking parameters, and to calibrate the weighting engine of
MannekenPix from user-supplied reference picks and related uncertainties. The calibration set
includes 1,329 reference picks and weights from myself, and it extends over the years 1984 to
1996. In order to evaluate the stability of the uncertainty predictions on totally unseen data, a
small out-of-sample or validation set of 226 reference picks has also been created from
seismograms spanning the 1997-2001 period.
The calibration and validation reference picks were performed with program Visual Picker 1.2 in
which most functions of MannekenPix are implemented with a graphical interface. Since the best
automatic picking results are expected from Wiener-filtered seismograms, the reference picking
was also done on Wiener-filtered seismograms. This does not imply that a bias in favor of the
automatic picking has been introduced, it means that a common de-noising technique has been
used in both cases. This is extremely important because a precise calibration of the weighting
engine is only possible if the human analyst and MannekenPix see sufficiently similar
seismograms. In order to ease the visual quantification of the uncertainties, Visual Picker plots
the uncertainty intervals on the seismograms during the picking process (Figure 4.3). All the
reference picking was done with picking weights ranging from 1 to 5 (Table 4.1) but no weight 5
picks were included in the reference sets. Poor discriminating results from MannekenPix
between picking weight 1 and weight 2 required the merging of these two groups into a single
69
N e t IL
S ta H M D T
Comp V
D a te 0 1 M A R 2 0 0 0
R e f T im e 2 0 :0 7 :5 5 .4 3 7
E p i 2 0 .0 k m
D e p 5 .0 k m
M a g 2 .8
2 .5 0 0
2 .0 0 0
1 .5 0 0
1 .0 0 0
Amplitude (V)
0 .5 0 0
(a)
0 .0 0 0
-0 .5 0 0
-1 .0 0 0
-1 .5 0 0
-2 .0 0 0
-2 .5 0 0
-3 .0 0 0
-3 .5 0 0
4 9 .6 0 0
4 9 .8 0 0
5 0 .0 0 0
5 0 .2 0 0
5 0 .4 0 0
5 0 .6 0 0
T im e ( s e c )
N e t IL
S ta N O H
Comp V
D a te 0 5 N O V 1 9 8 4
R e f T im e 0 1 :4 4 :1 9 . 4 2
E p i 1 6 3 .4 k m
D e p 2 .0 k m
M a g 0 .0
0 .3 0 0
0 .2 5 0
0 .2 0 0
0 .1 5 0
0 .1 0 0
0 .0 5 0
0 .0 0 0
Amplitude (V)
-0 .0 5 0
(b)
-0 .1 0 0
-0 .1 5 0
-0 .2 0 0
-0 .2 5 0
-0 .3 0 0
-0 .3 5 0
-0 .4 0 0
-0 .4 5 0
-0 .5 0 0
-0 .5 5 0
-0 .6 0 0
-0 .6 5 0
2 8 .0 0 0
N e t IL
2 8 .2 0 0
S ta H R I
C omp V
2 8 .4 0 0
2 8 .6 0 0
T im e ( s e c )
D a te 3 0 N O V 1 9 8 7
2 8 .8 0 0
R e f T im e 0 2 :5 2 :0 6 .5 6 7
2 9 .0 0 0
E p i 1 4 0 .8 k m
D e p 2 .0 k m
2 9 .2 0 0
M a g 2 .1
0 .1 6 0
0 .1 4 0
0 .1 2 0
0 .1 0 0
0 .0 8 0
0 .0 6 0
0 .0 4 0
0 .0 2 0
Amplitude (V)
0 .0 0 0
(c)
-0 .0 2 0
-0 .0 4 0
-0 .0 6 0
-0 .0 8 0
-0 .1 0 0
-0 .1 2 0
-0 .1 4 0
-0 .1 6 0
-0 .1 8 0
-0 .2 0 0
-0 .2 2 0
-0 .2 4 0
-0 .2 6 0
4 2 .2 0 0
N e t IL
S ta A T Z
4 2 .4 0 0
C omp V
4 2 .6 0 0
D a te 2 1 D E C 1 9 8 8
4 2 .8 0 0
T im e ( s e c )
R e f T im e 0 0 : 2 2 :1 8 .8 8 3
4 3 .0 0 0
E p i 7 5 .4 k m
D e p 9 .0 k m
4 3 .2 0 0
4 3 .4 0 0
M a g 1 .7
0 .1 8 0
0 .1 6 0
0 .1 4 0
0 .1 2 0
0 .1 0 0
0 .0 8 0
Amplitude (V)
0 .0 6 0
(d)
0 .0 4 0
0 .0 2 0
0 .0 0 0
-0 .0 2 0
-0 .0 4 0
-0 .0 6 0
-0 .0 8 0
-0 .1 0 0
-0 .1 2 0
2 7 .5 0 0
2 8 .0 0 0
2 8 .5 0 0
2 9 .0 0 0
2 9 .5 0 0
T im e ( s e c )
3 0 .0 0 0
3 0 .5 0 0
3 1 .0 0 0
Figure 4.3 Examples of Picking Weights 1-4. (a) Picking Weight 1. (b) Picking Weight 2. (c) Picking Weight 3.
(d) Picking Weight 4. Reference picks in magenta, routine picks in dark blue. The external solid lines (purple) on
both sides of the reference picks delineate the actual uncertainty limits while the finely dotted inner lines (purple)
delineate the limits of the previous (lower uncertainty) weight group.
70
weight 1 group. The weights used by MannekenPix for the Dead Sea area are the target weights
reported in Table 4.1.
Table 4.1 Uncertainty groups
1
Target Weight1
Uncertainty ε (ms)
Picking Weight
0 ≤ | ε | ≤ 20
1
20 < | ε | ≤ 40
2
40 < | ε | ≤ 80
3
2
80 < | ε | ≤ 140
4
3
| ε | > 140
5
4
1
Only the target weight is used for calibration and prediction.
The automatic filtering and picking of the complete data set with MannekenPix 1.7.6 took on the
average 0.4 sec per seismogram (2.5 seismograms / sec, or 9,000 seismograms / hour) with a 1.4
GHz Pentium 4 processor, and Linux as operating system.
4.2 DATA SET CHARACTERIZATION
As mentioned in 3.1, a description of the main properties of automatically picked data sets is
essential to potential users since by analogy with known cases they can then better decide if the
technique might be useful to them. This is very easy to do with MannekenPix since the program
provides various signal-to-noise ratios along with dominant frequencies for the signal and for the
noise.
Figure 4.4 displays the distance distribution for the complete data set and for the calibration set.
The range of epicentral distances for the complete data set (Figure 4.4a) is about 0-340 km. The
seismicity occurs throughout the crust (0-32 km) but the mantle is apparently aseismic. The
routine picking hit rate is 45.2 % of the total number of seismograms and routine picking extends
about as far as the seismogram distance range. The number of seismograms culminates between
80 and 90 km while the routine picking rate culminates at closer range, between 40 and 50 km.
The automatic picking hit rate is 46.5 % of the complete data set and it slightly exceeds (+1.3 %)
the routine picking rate. The distance distribution differs however more clearly between the
routine picking and the automatic picking. There are more routine picks between 0 and 90 km
71
1000
1000
Complete Data Set
Seismograms: 15,250
Routine Picks: 6,889
Hit Rate: 45.2 %
Automatic Picks: 7,089
High-Accuracy Mode
Hit Rate: 46.5 %
900
800
700
900
800
700
600
600
500
500
400
400
300
300
200
200
100
100
0
(a)
0
0
50
100
150
200
250
300
Epicentral Distance (km)
150
150
140
Calibration Set
Reference Picks: 1,329
Routine Picks: 1,213
Hit Rate: 91.3 %
Automatic Picks: 1,232
High-Accuracy Mode
Hit Rate: 92.7 %
130
120
110
100
130
120
110
100
90
90
80
80
70
70
60
60
50
50
40
40
30
30
20
20
10
10
0
(b)
140
0
0
50
100
150
200
250
300
Epicentral Distance (km)
Figure 4.4 Distance distribution of the number of seismograms and P picks. (a) Complete data set. (b) Calibration
set extracted from the complete data set.
but there are more automatic picks between 90 and 340 km. Figure 4.4b shows that the
calibration set is rather similar to the routinely picked seismograms of the complete set in terms
of distance range. The range is however a bit shorter as it does not exceed 270 km. On the other
hand, the calibration set is smoother than the complete data set in terms of distance incidence on
the hit rate. The average routine picking hit rate is 91.3 % of the reference picks while the
72
average automatic picking rate is 92.7 %. The automatic picking slightly exceeds (+1.4 %) here
also the routine hit rate.
An overall Signal-To-Noise ratio measured on the unfiltered seismograms is displayed for the
complete data set in Figure 4.5a. This is a very simple RMS signal-to-noise ratio evaluated in the
time domain around the routine pick times. It represents mainly the SNR of unfiltered
seismograms that can be picked. Large safety gaps between the mixed signal-and-noise
estimation window and the noise estimation window prevent against contamination from routine
picking errors. The mean SNR is 11.0 dB with a standard deviation of 12.5 dB. Some very low
SNR (-20 to -40 dB) are not erroneously reported. The frequency contrast between highfrequency signal and low-frequency noise of high-amplitude is sometimes sufficient to allow
some manual picking at these very low SNR.
Figure 4.5b displays the dominant frequencies of noise and signal evaluated around the routine
pick times. The dominant frequencies of the noise were determined on unfiltered seismograms
while the dominant frequencies of the signal were determined on Wiener-filtered seismograms.
Large safety gaps were also used here. The dominant noise is below 2 Hz on most seismograms
and the number of seismograms decreases regularly above 2 Hz until a background level reached
at about 5 Hz. The background level of noise is low but non-neglectable until 25 Hz. Since
dominant frequencies contain the highest spectral power for a given data segment, this means
also that an adaptive Wiener filter is preferable for this data set and not only a high-pass Wiener
filter as suggested by Douglas (1997). Dominant frequencies of the signal culminate between 5.5
and 6.0 Hz and decrease in a triangular way on both sides of the modal value. The signal extends
also toward higher frequencies, but in a less pronounced way than the noise does.
The impact of the Wiener filter on the SNR is displayed in Figure 4.6. The unfiltered calibration
set has a mean SNR of 16.3 dB and a standard deviation of 11.2 dB. This mean value is about 5
dB higher than the mean value of the complete data set. The fact that the SNR was estimated for
the complete set at the routine time while the impact of the Wiener filter is estimated at the
reference time is not an issue. Both means are within 0.5 Hz and their standard deviations differ
by less than 10 %. The global impact of the filter is to increase the mean SNR by 4.3 dB and by
reducing the standard deviation by about 25 %. Naturally, the effect of the Wiener filter is on the
average more pronounced for low SNR than for high SNR, and the distribution of filtered
seismograms is deeply skewed toward higher SNR. The three-parameter Gompertz regression
displayed in Figure 4.6b provides an estimate of the SNR increase as a function of the unfiltered
SNR.
73
SNR (dB)
-40
500
400
-30
(SNR )
-20
-10
0
10
20
30
40
50
60
500
= 11.0 (dB)
(a)
Complete Data Set
Unfiltered: 6,732
σ ( SNR ) = 12.5 (dB)
400
300
300
200
200
100
100
0
0
-40
-30
-20
-10
0
10
20
30
40
50
60
SNR (dB)
1500
1500
1400
Complete Data Set
Noise: 6,831
Complete Data Set
Signal: 6,860
1300
1200
1300
1200
1100
1100
1000
1000
900
900
800
800
700
700
600
600
500
500
400
400
300
300
200
200
100
100
0
(b)
1400
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Frequency (Hz)
Figure 4.5 Signal-To-Noise ratio and dominant frequency distributions for the complete data set. (a) SNR
distribution at the routine P picks from unfiltered seismograms. (b) Dominant frequency of Noise (from unfiltered
seismograms) and dominant frequency of Signal (from WF seismograms) distributions at the routine P pick times.
74
SNR (dB)
-40
-30
-20
-10
0
10
20
30
40
50
60
150
150
(SNR )
Calibration Set
Unfiltered: 1,314
Calibration Set
Filtered: 1,314
(a)
= 20.6 (dB)
σ ( SNR ) =
8.6 (dB)
100
100
(SNR )
= 16.3 (dB)
σ ( SNR ) = 11.2 (dB)
50
50
0
0
-40
-30
-20
-10
0
10
20
30
40
50
60
SNR (dB)
SNRU (dB)
-20
-10
0
10
20
30
40
50
60
40
40
Calibration Set Filtered: 1,314
Three parameter Gompertz regression
35
SNRF - SNRU (dB)
y = 263.6e
−e
35
−⎜⎜ x + 66.0 ⎟⎟
⎝ −55.8 ⎠
⎛
30
(b)
⎞
30
25
25
20
20
15
15
10
10
5
5
0
0
-5
SNRF - SNRU (dB)
-30
-5
-30
-20
-10
0
10
20
30
40
50
60
SNRU (dB)
Figure 4.6 Impact of the Wiener filter on the Signal-To-Noise ratio in the calibration set. (a) Unfiltered and filtered
SNR estimated at the reference pick times. (b) SNR increase by filtering as a function of the SNR of the unfiltered
seismograms. SNRU and SNRF are the SNR of the unfiltered and filtered seismograms respectively.
75
4.3 PICKING RATE AND ACCURACY
Table 4.2 summarizes the picking rate on the three data sets. To speed up the reference picking
of the validation set, only seismograms were selected for which both a routine pick and an
automatic pick were known to exist from the automatic picking of the complete set. This
explains why a picking rate of 100 % is found on this set for the routine and automatic filtered
pickings. The validation set is not used to test the picking rate or the picking accuracy, it is only
used to test the predictive power of the calibrated weighting engine on unseen data. Since Visual
Picker does not display the automatic picking results obtained with MannekenPix, no picking
bias in favor of the automatic picking times or weights is introduced by the selection process
described here.
Table 4.2 Picking hits and hit rate
Set
Seismograms
Reference picks
1,329
226
15,250
1,329
226
1,555
Calibration
Validation
Complete
Routine picks
(Hit Rate)
1,213 (91.3 %)
226 (100.0 %)
6,889 (45.2 %)
Auto picks1 WF2
(Hit Rate)
1,232 (92.7 %)
226 (100.0 %)
7,089 (46.5 %)
Auto picks1 UF3
(Hit Rate)
1,098 (82.6%)
183 (81.0 %)
5,216 (34.2 %)
1
High-Accuracy Mode.
Wiener-Filtered.
3
Unfiltered.
2
As said earlier, the automatic picking hit rate on Wiener-filtered seismograms is slightly higher
than the routine hit rate. On the complete data set, there is a drop of about 25 % in the number of
automatically picked seismograms when the Wiener filter is not applied (Table 4.2). This
outlines the importance of the Wiener filter in terms of hit rate alone.
Table 4.3 Picking accuracy
Routine time – Reference time
Observations
Min (sec)
Max (sec)
Mean (sec)
STD (sec)
Calibration
1,213
-1.533
0.390
-0.037
0.121
Validation set
226
-0.523
0.278
-0.046
0.097
Complete set
1,439
-1.533
0.390
-0.038
0.118
Automatic time (WF1) – Reference time
Observations
Calibration
1,232
Validation
226
Complete
1,458
76
Table 4.3 - continued
Min (sec)
Max (sec)
Mean (sec)
STD (sec)
Automatic time (UF2) – Reference time
Observations
Min (sec)
Max (sec)
Mean (sec)
STD (sec)
1
Wiener-Filtered.
2
Unfiltered.
-0.500
0.800
0.007
0.066
-0.217
0.501
0.022
0.059
-0.500
0.800
0.009
0.065
Calibration
1,098
-0.500
0.901
0.027
0.092
Validation
183
-0.177
0.301
0.031
0.055
Complete
1,281
-0.500
0.901
0.028
0.087
The overall picking accuracy is summarized in Table 4.3. A clear pattern of the routine picking
compared to my own picking is the tendency of the former to occur too early. Examples like the
one displayed in Figure 4.3a abound and confirm the clear statistical tendency reported here.
From the calibration set, the average discrepancy with the reference picking is –0.037 sec, with a
standard deviation of 0.121 sec. The Wiener-filtered automatic picks are located much closer to
the reference picks. The average difference is +0.007 sec, with a standard deviation of only 0.066
sec. The slightly positive average difference is a small residue from the delay so typical of the
Baer-Kradolfer (1987) picking algorithm. The unfiltered automatic picking is less accurate, the
average difference being +0.027 sec, with a standard deviation of 0.092 sec. Its overall accuracy
is about intermediate between the routine picking and the Wiener-filtered automatic picking.
Figure 4.7 displays the discrepancies between the routine picking and the reference picking, and
between the automatic picking on Wiener-filtered seismograms and the reference picking. The
pattern of early picking (negative discrepancies) is clearly apparent for the routine picking, and
discrepancies of –0.4 sec are observed even at SNR above +30 dB on some unfiltered
seismograms. Since I picked or completely checked the picking and weighting of the calibration
set 5 times without any interaction with a location algorithm, my conclusion is that systematic
routine picking errors affect this data set. No such pattern is present in the automatic picking
results, even if a few outliers are observed on the positive side. These few outliers result from a
normal behavior of MannekenPix. Since the program applies a negative delay correction, I tuned
it internally to preferably produce late arrivals than early arrivals for which the delay corrections
would increase the picking error instead of reducing it. Tuning the picking algorithm to do so is
quite easy since this is already its natural tendency (see 3.3.3). Figure 4.8 displays (–0.5 to +0.5
77
SNRU (dB)
-40
-30
-20
-10
0
10
20
30
40
50
60
0.5
0.5
(a)
0.0
0.0
-0.5
-0.5
-1.0
-1.0
-1.5
-1.5
-40
-30
-20
-10
0
10
20
30
40
50
60
20
30
40
50
60
Routine Time -Reference Time (sec)
Routine Time -Reference Time (sec)
Calibration Set: 1,207
SNRU (dB)
SNRF (dB)
-40
-30
-20
-10
0
10
1.0
1.0
(b)
0.5
0.5
0.0
0.0
-0.5
-0.5
-1.0
-1.0
-1.5
-1.5
-40
-30
-20
-10
0
10
20
30
40
50
Automatic Time -Reference Time (sec)
Automatic Time -Reference Time (sec)
Calibration Set: 1,131
60
SNRF (dB)
Figure 4.7 Estimated picking errors of the calibration set as a function of the SNR. (a) Routine picking, SNR from
unfiltered seismograms around the routine pick time. (b) Automatic picking, SNR from Wiener-filtered
seismograms around the routine pick time.
78
600
600
= −0.037 sec
σ ( ∆t ) = 0.121sec
P Picks
500
(a)
500
400
400
300
300
200
200
100
100
0
P Picks
( ∆t )
Routine - Reference
Calibration Set
Routine Picks: 1,213
Hit Rate: 91.3 %
0
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
Time (sec)
600
( ∆t )
= 0.007 sec
σ ( ∆t ) = 0.066 sec
500
Automatic - Reference
Calibration Set
High-Accuracy Mode
Wiener-Filtered
Automatic Picks: 1,232
Hit Rate: 92.7 %
P Picks
400
(b)
500
400
300
300
200
200
100
100
0
P Picks
600
0
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
Time (sec)
600
( ∆t )
= 0.027 sec
σ ( ∆t ) = 0.092sec
500
Automatic - Reference
Calibration Set
High-Accuracy Mode
Unfiltered
Automatic Picks: 1,098
Hit Rate: 82.6 %
P Picks
400
(c)
500
400
300
300
200
200
100
100
0
P Picks
600
0
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
Time (sec)
Figure 4.8 Estimated picking errors of the calibration set. (a) Routine picking. (b) Automatic picking, WienerFiltered. (c) Automatic picking, unfiltered.
79
100
= −0.046 sec
σ ( ∆t ) = 0.097 sec
(a)
80
60
60
40
40
20
20
0
P Picks
P Picks
80
100
( ∆t )
Routine - Reference
Validation Set
Routine Picks: 226
0
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
Time (sec)
P Picks
( ∆t )
= 0.022sec
σ ( ∆t ) = 0.059 sec
Automatic - Reference
Validation Set
High-Accuracy Mode
Wiener-Filtered
Automatic Picks: 226
80
100
(b)
80
60
60
40
40
20
20
0
P Picks
100
0
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
Time (sec)
Figure 4.9 Estimated picking errors of the validation set. (a) Routine picking. (b) Automatic picking (Wienerfiltered).
sec) histograms of the estimated picking errors for the routine picking, and for the Wienerfiltered and unfiltered automatic pickings. Similar results are observed on the smaller validation
set (Figure 4.9) from which the unfiltered automatic picking results have been omitted.
Since reference picks are only available for a limited number of seismograms, one way to collect
information about the automatic picking accuracy for the complete data set is to compare the
routine picks to the automatic picks. This is done in Figure 4.10a without the contribution of the
calibration set, displayed in Figure 4.10b. If the automatic picks are more accurate than the
80
P Picks
800
= −0.077sec
σ ( ∆t ) = 0.166sec
γ ( ∆t ) = −2.3
Routine - Automatic
Complete Data Set
(Calibration Set excluded)
Routine Picks: 4,206
Automatic Picks: 4,206
High-Accuracy Mode
Wiener-Filtered
1000
800
600
600
400
400
200
200
0
(a)
P Picks
( ∆t )
1000
0
-1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0
0.1
0.2
0.3
0.4
0.5
Time (sec)
P Picks
250
300
( ∆t )
= −0.041sec
σ ( ∆t ) = 0.118sec
γ ( ∆t ) = −2.8
Routine - Automatic
Calibration Set
Routine Picks: 1,131
Automatic Picks: 1,131
High-Accuracy Mode
Wiener-Filtered
250
200
200
150
150
100
100
50
50
0
(b)
P Picks
300
0
-1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0
0.1
0.2
0.3
0.4
0.5
Time (sec)
Figure 4.10 Difference between the routine pick times and the automatic pick times. (a) Complete data set,
calibration set excluded. (b) Calibration set. γ is the skewness.
routine picks on the calibration set as previous results have shown, then it is very likely that they
will also be more accurate on the complete data set since the distribution of discrepancies
between automatic picks and routine picks is stable (Figure 4.10b and Figure 4.10a). This is not a
proof in itself but it indicates that the overall pattern existing between the automatic picks and
the routine picks is preserved when the picking is extended from the calibration set to the
complete data set. If the automatic picking is more accurate than the routine picking on the
calibration set, there is then no particular reason to believe that this might not be the case for the
complete data set as well.
81
4.4 PICKING UNCERTAINTY
The uncertainties determined visually on the 1,329 reference picks of the calibration set are
reported in Table 4.4. The target weight (TW) is the group membership that MannekenPix
should be able to predict from the set of 9 predictors defined in 3.3.4.
Table 4.4 Weights of the reference picking (calibration set)
0 ≤ | ε | ≤ 20 ms
20 < | ε | ≤ 40 ms
40 < | ε | ≤ 80 ms
80 < | ε | ≤ 140 ms
| ε | > 140 ms
PW 1
PW 2
PW 3
PW 4
PW 5
255
857
199
18
0
TW 1
TW 2
TW 3
TW 4
0 ≤ | ε | ≤ 40 ms
40 < | ε | ≤ 80 ms
80 < | ε | ≤ 140 ms
| ε | > 140 ms
1,112 (83.7 %)
199 (15.0 %)
18 (1.3 %)
0
PW Picking Weight.
TW Target Weight.
ε is the estimated uncertainty on the reference picking.
The determination of the target weights for the automatic picks of the calibration set requires the
definition of a rule derived from the automatic picking error ∆t (Automatic time – Reference
time) and from the uncertainty determined on the reference picks (the ε values in Table 4.1 and
4.4). The rule I adopted for the Dead Sea basin data is to select the target weight corresponding
to the greatest value between the absolute automatic picking error ∆t and the absolute reference
uncertainty ε . In other words, an automatic pick is given the same weight as the corresponding
reference pick as long as it is located inside the uncertainty window of the reference pick. If it is
located outside this uncertainty window, then the picking error prevails and is used to determine
the target weight.
The target weights determined according to this rule for the 1,232 automatic picks of the
calibration set are reported in Table 4.5. These target weights and corresponding predictors were
imported into SPPS and a discriminant analysis was performed. Among the numerous outputs of
such an analysis are Fischer’s linear discriminant coefficients that allow MannekenPix to make a
prediction of the target weights on unseen cases. Only a very small selection of results is
reported here.
82
Table 4.5 Target Weights of the automatic picking (calibration set)
TW 1
TW 2
TW 3
TW 4
0 ≤ | ε | ≤ 40 ms
40 < | ε | ≤ 80 ms
80 < | ε | ≤ 140 ms
| ε | > 140 ms
952 (77.3%)
176 (14.3%)
65 (5.3%)
39 (3.1%)
TW Target Weight.
Box’s M test examines the assumption of homogeneity of covariance matrices and it is also
sensitive to multivariate normality. The test is significant on this data set and this means that
covariance matrices differ between groups, violating one assumption of discriminant analysis.
Discriminant analysis is however usually robust when the homogeneity of variances is not met.
An Anova test of equality of group means (Table 4.6) reveals that Wilks’ Lambda is significant
by the F test (at the 0.05 level) for all variables except GPDLDELF. Since group means do not
differ significantly for this variable, GPDLDELF is probably a useless predictor on this data set.
Table 4.6 Tests of Equality of Group Means
Predictor
Wilks' Lambda
F
Degrees of Freedom Significance
WFILSTON
.918 36.427
3
1,228
.000
GPDLSTON
.811 95.211
3
1,228
.000
GPDLAMPR
.814 93.769
3
1,228
.000
GPDLSIGF
.923 33.927
3
1,228
.000
GPDLDELF
.999
0.300
3
1,228
.825
THRCFRAT
.866 63.564
3
1,228
.000
PCABOTHR
.929 31.404
3
1,228
.000
PCBELTHR
.794 106.358
3
1,228
.000
CFNOIDEV
.943 24.965
3
1,228
.000
The standardized canonical discriminant function coefficients (Table 4.7) indicate the relative
importance of the independent variables in predicting the dependent variable. Very small value
for variable GPDLDELF confirm the limited interest of this predictor. Table 4.7 suggests that
GPDLSIGF might also be of little use on this data set.
83
Table 4.7 Standardized Canonical Discriminant Function Coefficients
Predictor
Function 1
Function 2
Function 3
WFILSTON
.239
-.038
.925
GPDLSTON
-.263
.677
-1.028
GPDLAMPR
-.361
-.520
1.879
GPDLSIGF
-.019
-.278
-.280
GPDLDELF
.067
.064
.092
THRCFRAT
.055
.568
-1.209
PCABOTHR
.297
.864
.040
PCBELTHR
.651
.140
-.126
CFNOIDEV
.139
-.160
.731
The prediction results are reported in a confusion matrix (Table 4.8). Values on the main
diagonal represent accurate predictions while off-diagonal values represent mis-classifications. A
global rate of 66.8 % of cases is accurately classified.
Table 4.8 Confusion matrix (9 predictors)
MPXW 1
MPXW 2
MPXW 3
MPXW 4
Total
Count TW 1
708
115
109
20
952
TW 2
35
79
48
14
176
TW 3
18
17
22
8
65
TW 4
7
10
8
14
39
TW 1
74.4
12.1
11.4
2.1 100.0
TW 2
19.9
44.9
27.3
8.0 100.0
TW 3
27.7
26.2
33.8
12.3 100.0
TW 4
17.9
25.6
20.5
35.9 100.0
%
66.8% of original grouped cases correctly classified.
TW Target Weight.
MPXW MannekenPix predicted Weight.
Variables GPDLDELF and GPDLSIGF have then been excluded from the pool of predictors and
a second analysis with the resulting 7 predictors has been performed. Original and crossvalidated (jackknife) confusion matrices are reported in Table 4.9. The results are only
84
marginally better than with all 9 predictors. The cross-validation confusion matrix does not
suggest that over-fitting might be an issue.
Table 4.9 Confusion matrices (7 predictors)
MPXW 1 MPXW 2 MPXW 3 MPXW 4 Total
Original
Count TW 1
709
122
103
18
952
TW 2
34
79
51
12
176
TW 3
17
16
22
10
65
TW 4
7
10
7
15
39
767
(62.3 %)
227
(18.3 %)
183
(14.9 %)
55 1232
(4.5 %)
TW 1
74.5
12.8
10.8
1.9 100.0
TW 2
19.3
44.9
29.0
6.8 100.0
TW 3
26.2
24.6
33.8
15.4 100.0
TW 4
17.9
25.6
17.9
38.5 100.0
Count TW 1
708
122
103
19
952
TW 2
34
78
51
13
176
TW 3
17
19
19
10
65
TW 4
7
10
7
15
39
TW 1
74.4
12.8
10.8
2.0 100.0
TW 2
19.3
44.3
29.0
7.4 100.0
TW 3
26.2
29.2
29.2
15.4 100.0
TW 4
17.9
25.6
17.9
38.5 100.0
Total
%
Cross-validated
%
67.0% of original grouped cases correctly classified.
66.6% of cross-validated grouped cases correctly classified.
In cross-validation, each case is classified by the functions derived from all cases other than
that case.
Figure 4.11 is a visual display of the confusion matrix. Considerable smearing from the main
diagonal values is observed for all target weights but the modal value of each row is always
located on the main diagonal. This means that within each target weight group, the mode of
85
Figure 4.11 Confusion matrix (7 predictors).
classified cases occurs in the correct predicted weight. Of a higher interest to a seismologist is
the content of each predicted weight group since this is what MannekenPix will provide for each
automatic pick. This information is contained in the columns of the confusion matrix and it is
specifically displayed in Figure 4.12. It is clear that target weight 1 data dominate predicted
weights 1 to 3. Predicted weight 1 has however an excellent distribution with only minor
contamination from target weights 3 and 4. Although dominated by the smearing from TW 1,
predicted weight 2 data appear also to be rather good. The composition of predicted weight 3
differs little from the composition of predicted weight 2 but I would not consider this group as
useless a priori. Predicted weights 4 are not dominated by the smearing of target weight 1 data
and represent a small part (4.5 %) of the automatically picked calibration data that should not
participate into any high-quality study. The automatic picking error content of the predicted
weight groups is displayed in Figure 4.13. It shows that predicted weight 3 differs perhaps here
86
800 150
MPXW 1 (767)
P Picks
600
600
500
500
400
400
300
300
200
200
100
100
0
2
3
MPXW 2 (227)
100
100
50
50
0
0
1
150
(b)
700
P Picks
(a)
700
P Picks
800
0
1
4
2
150 150
(c)
4
Target Weight
Target Weight
150
3
MPXW 4 (55)
100
50
0
1
2
3
P Picks
P Picks
100 100
P Picks
100
150
(d)
MPXW 3 (183)
50
50
0
0
50
0
4
1
2
Target Weight
3
4
Target Weight
Figure 4.12 Distribution of Target Weights in the Predicted Weights.
| Automatic Time - Reference Time | (msec)
0
100
200
300
400
| Automatic Time - Reference Time | (msec)
500
700
1
650
2
3
4
0
(a)
MPX W1 (767)
100
200
300
400
500
150
1
2
3
4
(b)
MPX W 2 (227)
600
550
500
100
400
P Picks
P Picks
450
350
300
250
50
200
150
100
50
0
0
0
100
200
300
400
500
0
100
| Automatic Time - Reference Time | (msec)
0
100
200
300
400
500
150
1
2
3
4
200
300
400
500
| Automatic Time - Reference Time | (msec)
0
MPX W 3 (183)
100
200
300
400
500
100
(c)
1
2
3
4
(d)
MPX W 4 (55)
P Picks
P Picks
100
50
50
0
0
0
100
200
300
400
500
0
| Automatic Time - Reference Time | (msec)
100
200
300
400
| Automatic Time - Reference Time | (msec)
Figure 4.13 Distribution of automatic picking errors in the Predicted Weights.
87
500
slightly more from predicted weight 2 by the higher rate of picking errors correctly identified as
belonging to predicted weight 3 group.
The confusion matrix from predictions made internally by MannekenPix on the validation set is
reported in Table 4.10. No significant deviation is observed globally from the confusion matrix
of the calibration set. An increase in the leakage from TW 1 toward MPXW 4 has however
occured.
Table 4.10 Confusion matrix of the validation set
MPXW 1
MPXW 2
MPXW 3
MPXW 4
Total
Count TW 1
126
22
21
11
180
TW 2
2
13
5
2
22
TW 3
3
2
8
3
16
TW 4
0
1
3
4
8
131
(57.8 %)
38
(16.8 %)
37
(16.4 %)
20
(8.9 %)
226
TW 1
70.0
12.2
11.7
6.1 100.0
TW 2
9.1
59.1
22.7
9.1 100.0
TW 3
18.8
12.4
50.0
18.8 100.0
TW 4
0
12.5
37.5
50.0 100.0
Total
%
66.8 % of original grouped cases correctly classified.
TW Target Weight.
The picking results for the complete data set are reported in Table 4.11. The complete data set
exhibits a significantly reduced rate of predicted weights 1 compared to the calibration set, about
the same rate of weights 2 and 3 as in the calibration set, and a much higher rate of weight 4
picks. Although a higher leakage from TW 1 to MPXW 4 was observed on the validation set, it
does not explain the significantly reduced rate of MPXW 1 and the increase in the number of
MPXW 4 values. The complete data set is more difficult to pick reliably for MannekenPix than
the calibration set.
Table 4.11 Predicted Weights of the automatic picking (complete data set)
MPXW 1
MPXW 2
MPXW 3
MPXW 4
3,058 (43.1 %)
1,173 (16.5 %)
1,554 (21.9 %)
1,304 (18.4 %)
88
4.5 A SIMPLE RELOCATION
A relocation of earthquakes from the calibration set has been performed using successively the
routine picks, the reference picks, and the automatic picks. The purpose of this simple relocation
is to see if some reduction in the RMS residual times is observed by re-picking the calibration
set. The original analyst weights have been applied for the routine picks, the target weights (TW)
have been applied for the reference picks and the predicted weights (MPXW) have been applied
for the automatic picks. Model Israel (see 2.3) was used and the relocations were performed with
Velest.
Table 4.12 Locatable earthquakes of the calibration set
Picking Type
Earthquakes
Locatable
Routine
Reference
114
Automatic
Not locatable
110 (96.5 %)
4 (3.5 %)
110 (96.5 %)
4 (3.5 %)
109 (95.6 %)
5 (4.4 %)
The number of locatable earthquakes is reported in Table 4.12 and does not differ significantly
between the three picking groups. The distribution of RMS residual times for the three
relocations is displayed in Figure 4.14.
The most important result is that the reference and automatic pickings display higher residual
times than the routine picking does, especially between 0.1 and 0.3 sec. This could imply that the
routine picking is more accurate as a whole than the reference picking. It can also imply that the
reference picking is more accurate than the routine picking but that the velocity structure of the
region imposes high residuals on earthquake locations derived from a simple 1-D model without
station corrections. Since we know that the Dead Sea region has a complex velocity structure
(see Chapter 2), higher residuals are not incompatible with a greater picking accuracy. In any
case, the convoluted interactions between arrival times, velocities and source locations can only
be properly understood if the picking is done objectively and is free from the attractive influence
of location results. The question of residual times appears to be a delicate issue here and it should
best remain open until a high-quality tomographic study including all relevant variables will shed
the appropriate light on the problem.
89
RMS residual time (sec)
RMS residual time (sec)
RMS residual time (sec)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
30
30
Earthquakes
30
Reference
Routine
Automatic
25
25
25
25
20
20
20
20
15
15
15
15
10
10
10
10
5
5
5
5
0
0
0
Earthquakes
30
0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
RMS residual time (sec)
RMS residual time (sec)
RMS residual time (sec)
Figure 4.14 Relocation residual times (calibration set)
The number of locatable earthquakes for the complete data set is reported in Table 4.13. The
number of locatable earthquakes derived from the automatic picking is only very slightly lower
than the number of locatable earthquakes derived from the routine picking.
Table 4.13 Locatable earthquakes of the complete data set
Picking Type
Routine
Automatic
Earthquakes
531
90
Locatable
Not locatable
528 (99.4 %)
3 (0.6 %)
526 (99.1 %)
5 (0.9 %)
Chapter 5
Conclusions
Lower-crustal strength under the Dead Sea basin
Conclusions about the lower-crustal seismicity of the Dead Sea basin were drawn in section 2.5
(pp. 19-21). Furthermore, results from Ginzburg and Ben-Avraham (1997) show that a major
basinal fault affecting the crystalline basement at 12-15 km depth runs exactly at the location (X
= 190, Y = 80 in Figure 2.4a) where a swarm of micro-earthquakes nucleate in the lower crust
below 25 km. This evidence suggests that major faulting in the Dead Sea basin extends probably
deeply into the lower crust. There is little doubt then that a joint study combining seismic
reflection profiles and earthquake focal mechanisms should be made at this location in an
attempt to relate the lower-crustal seismicity to the more superficial and better documented
tectonics. By such a study, further insight might be gained into the role played by lower-crustal
brittle failure in the development of the basin.
The rheological stratification of the lithosphere in the Dead Sea region should also be studied
further, preferably by several independent methods. For instance, the effective elastic plate
thickness could be derived from gravity data. On the other hand, postseismic relaxation studies
could also be performed, but as these studies depend critically on the occurrence of moderate to
large earthquakes (with long recurrence intervals along the DST), an unknown waiting time is
required. One study, from GPS data spanning only a short time window, has been performed in
the Middle-East (Piersanti et al., 2001) following the Mw = 7.2 Gulf of Aqaba-Elat earthquake of
November 1995. The best agreement with the data was obtained with a low viscosity value (1018
Pa s) for the lower crust and the asthenosphere, a result consistent with the higher heat flow (see
section 2.5) in the Gulf of Aqaba-Elat compared to the heat flow in the Dead Sea basin.
91
Following analytical and numerical models recently developed, Roy and Royden (2000a, 2000b)
suggest also that “when an elastic upper crust is underlain by a low-viscosity lower crust at a
strike-slip plate boundary, the deformation zone tends to be broad at the surface and
encompasses many parallel strike-slip faults in an interacting network. In contrast, when the
entire crust behaves elastically, the deformation zone remains narrow and focused on a single
plate-bounding fault, reflecting imposed mantle motions”. It would be interesting to apply these
models to the DST in the vicinity of the Dead Sea basin, and to compare the results with those
obtained for the Gulf of Aqaba-Elat. The relative simplicity of the DST in the vicinity of the
Dead Sea basin might well be closely related to the presence of a strong lower crust along this
segment of the plate boundary.
Several other methods can be used to better constrain the rheological properties of the lower
crust and the upper mantle, and new techniques are regularly proposed. The Dead Sea region
gives us a rare opportunity to better understand the properties of the tectonically active
continental lithosphere under a low heat flow regime. It would however not be wise to possibly
miss such an opportunity by reaching conclusions too soon about the rheological properties of
the uppermost mantle, for which we only know that it appears to be aseismic during 14 years.
This is especially true when taking into account the complexity of the problems involved and the
erroneous generalizations already made during the last 20 years regarding the rheology of the
continental lithosphere.
A new picking system: MannekenPix
The development of MannekenPix convinced me that many picking algorithms are not routinely
used on a large scale because the complementary components they need are just missing.
Designing a turn-key automatic picking package required me to work on a broad front of
problems, sometimes far from the central theme of automatic picking. An adaptive Wiener filter,
delay corrections and a sophisticated weighting engine were necessary ingredients to turn the
Baer-Kradolfer (1987) picking algorithm into a real production tool compatible with the stringent
requirements of high-quality studies. MannekenPix is still far from being an ideal automatic
picking system but I believe that as it is now, it may already benefit to a significant number of
applications ranging from automatic bulletin generation to automatic focal mechanism
determinations and high-quality tomographic studies.
92
For data sets in which the dominant frequencies of signal and noise are sufficiently distinct, the
automatic Wiener filter of MannekenPix can significantly increase the SNR of noisy
seismograms. Such a filter does neither affect significantly the amplitude of the signal nor does it
introduce delays or precursory sidelobes like sub-optimal filters generally do. For data sets in
which the dominant frequencies of signal and noise mainly overlap and no improvement by
traditional filtering is expected, the Wiener Filter of MannekenPix just leaves the original data
intact. The filter is probably too slow to be integrated as is in a near real-time picking system, but
it can run significantly faster with a minor trade-off in the search of the optimal SNR.
Another quality of MannekenPix is that its picking weights derive from true uncertainty classes
defined in time units. The weighting mechanism of MannekenPix attempts to predict the same
uncertainties as those that would be estimated by the analyst. As such, it acts as an extension of
manual weighting and not as a totally independent method possibly in conflict with the legacy.
Since MannekenPix weights can be computed very fast, any picking system (real-time or not)
could benefit from the method. However, the discrimination of quantitative time uncertainty
groups depends not only on the MannekenPix method of weighting but also on the availability of
adequate predicting variables. There is thus no guarantee that predictors of an existing picking
system can provide such discriminating power.
The long-term goal of automatic weighting should be perhaps to determine picking uncertainties
without any user-supplied reference weights. By doing so, another source of inconsistencies
might be removed from automatic picking data sets. One possible way to reach this difficult goal
requires however that the deconvolution by the seismograph response would be both routinely
feasible and useful within the framework of automatic picking.
The main strength of MannekenPix is probably its ability to provide a good rate of accurate
picks. About its limitations in the actual state, MannekenPix misses some arrivals that it should
not miss. The difficult problem of quantitatively weighting the picks needs also to be more
reliable, but the highest weight classes are however well insulated from largely erroneous picks.
Deconvolution
The main problem with the recording system is that it usually acts as an out-of-focus lens
through which everything appears blurred. Such a distortion implies a systematic reduction of the
signal-to-noise ratio, even in the absence of significant additive noise. Refocusing the signal by
93
the digital deconvolution of the instrumental response could significantly benefit to the accurate
picking and autonomous weighting of phases, but this possibility needs to be fully evaluated with
real-world data. From a practical standpoint, deconvolution should be largely feasible since the
instrumental response is usually well known for most data sets. This response may not be
perfectly stable over time but it is probably stable enough for the purpose of deconvolution. It
would also be interesting to investigate whether or not deconvolution has an incidence on the
detection rate of weak signals buried in noise.
Application of MannekenPix to the Dead Sea region
The application of MannekenPix to the Dead Sea local data convinced me also that the program
is able to detect and correct a significant number of systematic errors commonly present in data
sets. These errors do not only include large picking errors, they also include largely incorrect
observation weights. Naturally, the program also makes similar errors but in a limited way that
can be clearly assessed during the calibration of the weighting engine.
By using MannekenPix to pick the seismograms from well-constrained earthquakes of the Dead
Sea region, 526 (99.1 %) out of 531 earthquakes are locatable by automatic picking. Out of
15,250 seismograms, 6,889 (45.2 %) were routinely picked and 7,089 (46.5 %) could be picked
automatically. On the calibration data set, the average discrepancy between the routine picking
and the reference picking is –0.037 sec, with a standard deviation of 0.121 sec. The average
discrepancy of the automatic picking is +0.007 sec with a standard deviation of only 0.066 sec. A
clear pattern of early picking affects the routine picking of this data set while the automatic
picking discrepancies are significantly reduced and nearly randomly organized compared to
those of the routine picking.
For the complete data set, 3,058 phases (43.1 %) of the 7,089 automatic P picks fall into
predicted weight 1 (absolute uncertainty not greater than 40 msec), 1,173 (16.5 %) fall into class
2 (absolute uncertainty between 40 msec and 80 msec), 1,554 (21.9 %) fall into class 3 (absolute
uncertainty between 80 msec and 140 msec) and 1,304 (18.4 %) fall into class 4 (absolute
uncertainty greater than 140 msec). The results from a totally out-of-sample set of reference
picks and weights confirm the stability of predicted weights on unseen data.
94
The automatic filtering and picking of the complete data set with MannekenPix 1.7.6 took on the
average 0.4 sec per seismogram (2.5 seismograms / sec, or 9000 seismograms / hour) with a 1.4
GHz Pentium 4 processor, and Linux as operating system.
My understanding is that MannekenPix fulfilled the main purpose of this work, i.e. to provide a
set of picking data satisfying the quantity and quality requirements for a travel-time tomographic
study of the Dead Sea region.
Application of MannekenPix to the seismicity of Italy
Di Stefano et al. (2004, to be submitted) present the application of MannekenPix to about
240,000 seismograms from nearly 29,000 local earthquakes routinely recorded by the Italian
national seismic network during the period 1998-2001. A standard version of MannekenPix was
able to produce 103,131 P picks (73% of the 139,500 routine onsets) from 23,108 events out of
28,900 events.
While the bulletin readings are almost always un-weighted, MannekenPix distinguishes between
higher and lower quality picks. About 17,130 phases (17 %) out of the 103,131 fall into class 1
(absolute uncertainty not greater than 0.1 sec) and 15,429 phases (15 %) fall into class 2
(absolute uncertainty between 0.1 sec and 0.2 sec). These figures are slightly lower than for the
700 seismograms of the calibration set, possibly because a greater number of events of small
magnitude is present in the complete data set, yielding a much higher number of phases in class
4.
To test the re-picked data set we merged the 103,131 automatic picks with bulletin phases from
other networks included in the CSI bulletin (Catalogo della Sismicita' Italiana) and we relocated
the events following the same method and parameters used to generate the catalog. We replaced
all the INGV station bulletin readings with the automatic picks. Results displayed in Figure 5.1
show that MannekenPix arrival times for classes 1 and 2 combined, produce a distribution of
residual times with a much smaller standard deviation than for the CSI bulletin. This means that
a significant increase in the quality of the data set has been gained, coming at the price of a
reduced quantity. It is important to note that these results were obtained with MannekenPix 1.6.2
that does not include yet the secondary delay correction. The polarities provided by
MannekenPix make also the subset suitable for high-quality automatic focal mechanism
determinations on a large scale with respect to the bulletin.
95
The application of MannekenPix to the very large and inhomogeneous dataset of waveforms
recorded in Italy from 1998 to 2001 yields nearly 33,000 high-quality weighted picks and
polarities. By using MannekenPix we achieved our goal to build a new dataset of P-wave arrival
times and polarities belonging to user-defined classes 1 and 2 (the highest qualities) with
associated uncertainty estimates. The analysis of relocation residuals and the time versus
distance plots for these classes show the effectiveness of the picking system. Although the hit
rate of MannekenPix 1.6.2 applied to this large and noisy dataset did not exceed 75 % of the rate
of an expert seismologist, the consistency of the automatic arrivals and polarities and their rapid
estimation are very suitable to substitute bulletin data, solving the typical problem of extending
consistency and quality to large datasets. We believe that the improved seismic dataset is suitable
to refine the seismic tomography, and to improve the knowledge of the local and regional stress
fields in the Italian peninsula through the determination of a large number of focal mechanisms
derived from first-motion polarities determined automatically by MPX for well-constrained
events, and extending also the analysis to small magnitudes and past events.
Figure 5.1 Distribution of relocation residual times for INGV stations. (Left) MPX automatic picking residual
times. Classes 1-4 in black and classes 1-2 in gray. (Right) CSI bulletin residual times.
96
Appendix A
Abbreviations
AIC
AR
CSI
dB
DFT
DPSS
DST
FFT
FIR
FPE
GII
GPS
INGV
JSO
LET
LTA
MDA
MEM
MPXW
PSD
PW
RMS
SMA
SMSTD
An Information theoretic Criterion
Autoregressive
Catalogo della Sismicita' Italiana
decibel
Discrete Fourier Transform
Discrete Prolate Spheroidal Sequence
Dead Sea Transform
Fast Fourier Transform
Finite Impulse Response
Final Prediction Error
Geophysical Institute of Israel
Global Positioning System
Istituto Nazionale di Geofisica e Vulcanologia
Jordan Seismological Observatory
Local Earthquake Tomography
Long-Term Average
Multiple Discriminant Analysis
Maximum Entropy Method
MannekenPix Predicted Weight
Power Spectral Density
Picking Weight
Root Mean Square
Simple Moving Average
Simple Moving Standard Deviation
97
SNR
STA
STDB
TW
WSS
Signal-To-Noise Ratio
Short-Term Average
Simple Standard Deviation Band
Target Weight
Wide-Sense Stationarity
98
Appendix B
Source function parameters and seismograph response of
the Wiener-filtered synthetic example (Figure 3.6)
The displacement source function used to build the synthetic example of Figure 3.6 is plotted in
Figure B.1a. It was generated in Pitsa (Scherbaum and Johnson, 1992) according to Brune’s
model (Brune, 1970) but all other operations were performed in Matlab, mostly with functions of
the Signal Processing Toolbox. Stress drop, shear velocity and source radius have typical values
for a microearthquake of magnitude ML = 2 in the Dead Sea region (van Eck and Hofstetter,
1989). The value of the shear modulus corresponds to a source depth of 5-15 km (Turcotte and
Schubert, 2002). The displacement function has been truncated to a length of 200 msec, and the
corresponding velocity function is plotted in Figure B.1b. The sampling period is 10 msec
throughout the example. In order to build a P-wave pseudo-wavetrain, a series of spikes of
decreasing amplitude (Figure B.1c) was generated starting at time t = 7 sec of a 10 seconds
length simulation segment. The interval of time between spikes is 200 msec and equals the
duration of the truncated source functions.
The source velocity function was convolved by the spikes to produce the noiseless pseudowavetrain of Figure B.2a. Although the first spike is located exactly at time t = 7 sec, the
wavetrain at that time has a zero value. This results from the fact that the first sample of the
source velocity function has a zero value and that this value is preserved through the convolution
by a spike. By analogy of continuous functions, I consider the first-arrival time of a noiseless
wavetrain to be the last zero-valued sample of the pre-arrival segment and not the first sample
different from zero. This choice looks natural when seismograms are visualized in the
perspective of onset picking.
In order to add noise to the pseudo-wavetrain, 10 seconds of instrumentally recorded noise were
deconvolved by the response of a digital seismograph composed of a simulated Marks L4-C
99
Time t (msec)
50
100
150
200
σ r
u (t ) = 2 R (θ , φ ) vs te
µ z
-1
-1
-2
-2
Radiation pattern: R (θ , φ ) = −0.625
Stress drop: σ = 4 bars
Shear modulus: µ = 27 GPa
Shear velocity: vs = 3.6 km/s
Source radius: r = 0.2 km
Hypocentral distance: z = 20 km
-3
-4
-5
-3
-4
-5
-6
-6
0
50
100
150
200
100
100
0
Velocity (µm/sec)
(a)
(b)
0
-100
-100
-200
-200
-300
-300
-400
-400
-500
-500
0
50
100
150
Velocity (µm/sec)
Displacement u (µm)
0
v
−2.34 s t
r
Displacement u (µm)
0
0
200
Time (msec)
Time (sec)
0
1
2
3
4
5
6
7
8
9
10
1.0
1.0
0.5
0.5
0.0
0.0
-0.5
-0.5
-1.0
-1.0
0
1
2
3
4
5
6
7
8
9
(c)
10
Time (sec)
Figure B.1 Synthetic source function and convolution spikes. (a) Source function (displacement). (b) Source
function (velocity). (c) Convolution spikes. The time of first arrival is marked by the dark red line at time t = 7 sec.
The sampling period is 10 msec.
100
Time (sec)
2
3
4
5
6
7
8
9
10
500
400
400
300
300
200
200
100
100
0
0
-100
-100
-200
-200
-300
-300
-400
-400
-500
-500
500
500
0
0
-500
-500
(a)
Velocity (µm/sec)
1
(b)
Velocity (µm/sec)
Velocity (µm/sec)
Velocity (µm/sec)
0
500
500
500
0
0
-500
-500
0
1
2
3
4
5
6
7
8
9
Velocity (µm/sec)
Velocity (µm/sec)
(c)
10
Time (sec)
Figure B.2 Velocity signal, noise and noisy signal. (a) Noiseless synthetic pseudo-wavetrain signal (velocity). (b)
Deconvolved recorded seismic noise. (c) Combined signal (a) and noise (b). The time of first arrival is marked by
the dark red line at time t = 7 sec. The sampling period is 10 msec.
101
velocity seismometer and a digital 5th-order Butterworth low-pass (anti-aliasing) filter. The
response of this digital simulated seismograph is close to the response of the actual instruments
deployed by GII in the Dead Sea region (van Eck and Hofstetter, 1989), except for a high-pass
filter with corner frequency at 0.2 Hz that has been discarded here. The deconvolution was
performed by spectral division in Matlab with routine “Decon1” of seismological package Coral1
(Creager, 1997). The primary purpose of Decon1 is to compute receiver functions (Langston,
1979) but nothing prevents other uses like the one described here. Deconvolving the recorded
noise by the seismograph response serves to better simulate true ground noise, the noise that
mixes with the signal before both are filtered by the seismograph during the recording process.
The result is plotted in Figure B.2b. The noiseless signal (Figure B.2a) and the deconvolved
noise (Figure B.2b) were then added together. The result is the noisy signal plotted in Figure
B.2c. All plots in Figure B.2 are supposed to be free of instrumental distortions and are
expressed as ground velocity.
The seismograph response has already been used to deconvolve the instrumentally recorded
noise segment but no details were provided about how this response was obtained.
The discrete velocity impulse response of a standard Marks L-4C seismometer can be
determined (Scherbaum, 1996) from the analog zeros and poles provided by the manufacturer
(Table B.1). I did this in Matlab by computing the transfer function T ( s ) from the analog zeros
and poles with function “zp2tf”, and by mapping T ( s ) onto the discrete transfer function T ( z )
by the bilinear transformation (function “bilinear” in Matlab). An arbitrary generator constant G
= 1.0 [V/(m/sec)] was used. The discrete impulse response and frequency response are then
given by functions “impz” and “freqz” respectively. The results are plotted in Figure B.3.
Table B.1 Zeros and Poles of the Marks L-4C
Zero
Pole
0 + 0i
- 4.443 + 4.443 i
0 + 0i
- 4.443 - 4.443 i
Eigenfrequency f c = 1.0 Hz , Damping h = 0.707 .
1
http://www.ess.washington.edu/Faculty/creager/
102
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
-0.1
0
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
-0.1
(a)
0
(b)
50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800
Time (msec)
Frequency (Hz)
0.1
1
10
Magnitude (dB)
fc
-10
-10
-20
-20
-30
-30
-40
-40
-50
-50
-60
-60
-70
-70
-80
Magnitude (dB)
0.01
0
-80
0.01
0.1
1
10
Frequency (Hz)
40
50
10
180
150
150
120
120
Phase (deg)
(c) 180
90
90
fc
60
60
30
30
0
0
10
20
30
40
50
30
40
50
30
30
(d)
25
25
20
fc
20
15
15
10
10
fc
5
5
0
0
10
Frequency (Hz)
20
Group delay (samples)
30
Group delay (samples)
20
Phase (deg)
10
20
30
40
50
Frequency (Hz)
Figure B.3 Digital simulated L4-C velocity seismometer. (a) Velocity impulse response. (b) Magnitude spectrum.
(c) Phase spectrum. (d) Group delay spectrum. The sampling period is 10 msec.
103
0.30
0.30
0.25
0.25
0.20
0.20
0.15
0.15
0.10
0.10
0.05
0.05
0.00
0.00
-0.05
-0.05
-0.10
-0.10
0
50
100
150
200
(a)
250
Time (msec)
Frequency (Hz)
10
Magnitude (dB)
0
fc
-100
-100
-200
-200
-300
-300
-400
-400
1
(b)
Magnitude (dB)
1
0
10
Frequency (Hz)
30
40
50
-90
-180
-180
fc
-270
-270
-360
-360
-450
Group delay (samples)
-90
Phase (deg)
10
-450
10
20
30
40
20
30
40
50
10
0
Phase (deg)
(c)
20
5
5
fc
0
10
Frequency (Hz)
(d)
fc
0
50
10
Group delay (samples)
10
0
20
30
40
50
Frequency (Hz)
Figure B.4 Digital 5th-order Butterworth anti-aliasing filter. (a) Impulse response. (b) Magnitude spectrum.
(c) Phase spectrum. (d) Group delay spectrum. The sampling period is 10 msec.
104
0.25
0.20
0.15
0.10
0.05
0.00
-0.05
-0.10
-0.15
-0.20
0.25
(a)
0.20
0.15
0.10
0.05
0.00
-0.05
-0.10
-0.15
-0.20
0
200
400
600
800
Time (msec)
Frequency (Hz)
1
10
0
fc
Magnitude (dB)
fc
-50
-50
-100
-100
0.1
1
(b)
Magnitude (dB)
0.1
0
10
Frequency (Hz)
30
40
50
10
20
30
40
50
35
35
(d)
90
90
30
30
0
0
25
25
20
20
15
15
-90
-90
-180
-180
-270
-270
-360
-360
-450
-450
Group delay (samples)
180
Phase (deg)
Phase (deg)
(c)
20
Group delay (samples)
10
180
10
10
fc
5
5
0
10
20
30
40
50
0
10
Frequency (Hz)
20
30
40
50
Frequency (Hz)
Figure B.5 Simulated seismograph. (a) Impulse response. (b) Magnitude spectrum. (c) Phase spectrum. (d) Group
delay spectrum. The sampling period is 10 msec.
105
The 5th-order Butterworth digital anti-aliasing filter with corner frequency f c = 12.5 Hz was
computed with function “butter” of Matlab. This function creates a Butterworth analog low-pass
filter, and converts this analog filter into a digital filter through a bilinear transformation with
warped corner frequency. The discrete impulse response and frequency response are then given
by functions “impz” and “freqz” as for the seismometer. The results are plotted in Figure B.4.
The seismograph response (combined L4-C and anti-aliasing filter) is plotted in Figure B.5. The
simulated seismogram of Figure 3.6a was finally obtained by convolving the noisy signal (Figure
B.2c) by the seismograph impulse response (Figure B.5a). The first 0.6 seconds of the noiseless
signal filtered by the seismograph (the “recorded” signal) and the noiseless true signal are plotted
in Figure B.6. It shows clearly how the true signal is distorted by the seismograph during the
recording process.
Time (sec)
6.8
6.9
7.0
7.1
7.2
7.3
7.4
7.5
7.6
200
700
600
150
500
400
100
200
50
100
0
0
-100
-50
-200
-300
-100
-400
-500
-150
-600
-700
-200
6.8
6.9
7.0
7.1
7.2
7.3
7.4
7.5
7.6
Time (sec)
Figure B.6 Noiseless signal (detail). The recorded signal (Voltage) is in black and the corresponding true signal
(Velocity) is in gray. The sampling period is 10 msec.
106
Velocity (µm/sec)
Voltage (µV)
300
Appendix C
GII and JSO Station Coordinates
C.1 GII STATIONS
GII stations have been primarily located in the past in the (X,Y) Rectangular Israel Grid. Highly
accurate formulas from the Survey of Israel were used to convert between the Israel Grid
coordinates and Geographical coordinates (Cassini-Soldner projection). Round-trip conversions
on reference points are accurate at ± 0.02 m. For field locations where the station name has
changed once or several times over the years, only the most recent known name is reported here.
Table C.1 GII station coordinates
Station
ADI
ARAD
ARVA
ARVI
ASHL
ASI
ATAR
ATR
ATZ
BGIO
BLVR
BRNI
BSO
CRI
DAM3
DLIA
DOR
X (km)
171.570
178.800
197.550
168.000
116.500
159.200
97.300
115.600
175.510
158.490
199.000
149.600
101.600
153.860
192.350
156.000
120.720
Y (km)
276.080
70.000
135.000
5.600
46.500
82.100
48.700
42.000
247.590
125.560
222.000
238.100
75.550
231.990
54.500
221.000
102.120
107
Elevation (m)
469
160
-330
0
290
850
200
350
515
760
275
400
140
431
-390
160
182
Latitude (°N) Longitude (°E)
33.0797
35.2262
31.2212
35.3018
31.8071
35.5004
30.6403
35.1886
31.0080
34.6492
31.3303
35.0960
31.0268
34.4480
30.9674
34.6401
32.8228
35.2682
31.7222
35.0880
32.5917
35.5183
32.7370
34.9918
31.2692
34.4912
32.6820
35.0373
31.0812
35.4437
32.5829
35.0603
31.5098
34.6907
Table C.1 - continued
Station
DRGI
DS10
DS11
DS12
DS13
DS6
DSD2
DSI
EIL
ENGI
GLH
GVI
GVMR
HAF
HAMT
HLZ
HMDT
HNTI
HRI
HRSH
JVI
KER
KMTI
KOMT
KRPI
KSDI
KSHT
KZIT
MAMI
MBH
MGI
MKT
MMLI
MMR
MNFI
MNIT
MOI
MRN
MSDA
MSH
MZDA
NEOT
NOH
NSH
X (km)
187.380
187.640
197.480
191.930
190.490
187.770
191.800
186.600
145.000
187.400
211.230
141.510
187.330
152.700
147.450
116.000
198.730
166.000
218.760
175.740
182.460
101.790
123.100
175.400
202.800
211.807
226.050
92.200
163.870
141.550
190.300
164.430
188.840
187.970
172.500
153.740
182.800
186.600
177.350
129.890
184.450
186.800
146.130
148.000
Y (km)
111.060
112.020
134.460
125.400
119.900
71.090
65.000
108.580
-101.800
97.600
235.530
115.760
219.030
242.600
-115.400
112.000
185.120
277.200
296.860
233.650
149.030
45.310
-54.400
59.000
206.000
288.643
265.710
36.500
212.290
-88.400
206.400
39.720
204.840
266.130
250.750
207.800
127.000
268.400
80.450
45.280
79.500
43.490
11.250
136.000
108
Elevation (m)
10
20
-373
9
169
-390
-390
200
200
-300
335
389
95
186
0
100
125
250
1014
416
686
363
450
200
-250
170
700
200
461
842
400
517
508
1100
350
118
450
900
400
364
-300
-390
680
300
Latitude (°N) Longitude (°E)
31.5914
35.3925
31.6001
35.3953
31.8022
35.4996
31.7207
35.4408
31.6711
35.4255
31.2309
35.3960
31.1759
35.4381
31.5690
35.3843
29.6712
34.9512
31.4700
35.3925
32.7133
35.6491
31.6336
34.9091
32.5651
35.3939
32.7776
35.0247
29.5485
34.9768
31.5987
34.6404
32.2591
35.5143
33.0898
35.1665
33.2660
35.7327
32.6971
35.2706
31.9339
35.3412
30.9965
34.4953
30.0981
34.7229
31.1220
35.2661
32.4473
35.5582
33.1922
35.6577
32.9848
35.8090
30.9164
34.3956
32.5044
35.1442
29.7920
34.9152
32.4512
35.4253
30.9481
35.1512
32.4371
35.4097
32.9898
35.4016
32.8513
35.2361
32.4639
35.0365
31.7352
35.3445
33.0103
35.3870
31.3154
35.2867
30.9975
34.7895
31.3068
35.3612
30.9820
35.3853
30.6910
34.9603
31.8162
34.9771
Table C.1 - continued
Station
OFRI
PRNI
RAMI
RMN
RMNI
RTMM
SAGI
SDOM
SHLH
SHZF
SVTA
SZAF
YAIR
YASH
YTIR
ZEFH
ZELM
ZFRI
ZNT
X (km)
149.083
150.300
161.420
115.460
127.000
119.590
118.800
186.660
105.900
106.250
114.060
107.280
182.000
138.200
160.980
140.690
105.500
166.950
152.780
Y (km)
224.881
-26.360
243.500
-8.420
1.000
51.060
-42.400
54.100
45.050
34.200
38.320
34.510
70.400
-112.700
84.620
-118.320
56.500
-2.850
182.890
Elevation (m)
100
412
37
1003
880
259
560
-164
310
300
370
293
80
680
905
118
215
0
230
Latitude (°N) Longitude (°E)
32.6178
34.9865
30.3518
35.0046
32.7859
35.1178
30.5126
34.6413
30.5980
34.7611
31.0493
34.6814
30.2062
34.6777
31.0777
35.3840
30.9944
34.5383
30.8965
34.5427
30.9341
34.6241
30.8994
34.5534
31.2247
35.3354
29.5727
34.8813
31.3530
35.1146
29.5220
34.9072
31.0976
34.5334
30.5641
35.1777
32.2392
35.0267
C.2 JSO STATIONS
JSO station coordinates are given by JSO in Geographical coordinates. Conversion to
Rectangular Israel Grid coordinates was made with the same conversion formulas as those in
C.1.
Table C.2 JSO station coordinates
Station
AQBJ
DHLJ
HSHJ
KFNJ
LISJ
MASJ
MKRJ
MRSJ
NAQJ
SALJ
X (km)
154.570
188.424
187.450
214.156
195.871
218.105
210.979
180.891
198.323
214.776
Y (km)
-95.573
25.538
-129.466
141.143
72.117
126.391
106.757
-100.290
-65.543
157.469
109
Elevation (m)
170
-80
1170
-90
-327
783
815
810
1640
780
Latitude (°N) Longitude (°E)
29.7275
35.0500
30.8200
35.4020
29.4217
35.3893
31.8620
35.6760
31.2400
35.4810
31.7288
35.7170
31.5520
35.6410
29.6850
35.3220
29.9982
35.5030
32.0092
35.6833
References
Akaike, H. (1969) Fitting autoregressive models for prediction. Annals of the Institute of
Statistical Mathematics, 21, 243-247.
Akaike, H. (1974) A New Look at the Statistical Model Identification. IEEE Transactions on
Automatic Control, AC-19, 716-723. Reprinted in Childers, D.G. (Ed.) (1978) Modern
spectrum analysis: IEEE Press, New York, NY, 234-241.
Aki, K., and Richards, P. (1980) Quantitative Seismology, Theory and Methods. W.H. Freeman,
San Francisco, CA.
Aldersons, F., Ben-Avraham, Z., Hofstetter, A., Kissling, E., and Al-Yazjeen, T. (2003) Lowercrustal strength under the Dead Sea basin from local earthquake data and rheological
modeling. Earth and Planetary Science Letters, 214, 129-142.
Allen, R. (1978) Automatic earthquake recognition and timing from single traces. Bulletin of the
Seismological Society of America, 68, 1521-1532.
Allen, R. (1982) Automatic phase pickers: their present use and future prospects. Bulletin of the
Seismological Society of America, 72, S225-S242.
Al-Zoubi, A., and Ben-Avraham, Z. (2002) Structure of the earth’s crust in Jordan from potential
field data. Tectonophysics, 346, 45-59.
Al-Zoubi, A., and ten Brink, U. (2002) Lower crustal flow and the role of shear in basin
subsidence: an example from the Dea Sea basin. Earth and Planetary Science Letters, 199,
67-79.
Andersen, N. (1974) On the calculation of filter coefficients for maximum entropy spectral
analysis. Geophysics, 39, 1, 69-72. Reprinted in Childers, D.G. (Ed.) (1978) Modern
spectrum analysis: IEEE Press, New York, NY, 252-255.
Anderson, E.M. (1951) The Dynamics of Faulting, 2nd edition. Oliver and Boyd, Edinburgh,
England.
110
Aster, R., and Rowe, C. (2000) Automatic phase pick refinement and similar event association in
large seismic datasets. In Thurber, C.H., and Rabinowitz, N., (Eds.) Advances in seismic
event location: Kluwer Academic Publishers, Doordrecht, Modern approaches in geophysics,
18, 231-263.
Baer, M., and Kradolfer, U. (1987) An automatic phase picker for local and teleseismic events.
Bulletin of the Seismological Society of America, 77, 1437-1445.
Baggeroer, A.B. (1976) Confidence Intervals for Regression (MEM) Spectral Estimates. IEEE
Transactions on Information Theory, IT-22, 534-545. Reprinted in Childers, D.G. (Ed.)
(1978) Modern spectrum analysis: IEEE Press, New York, NY, 150-161.
Banda, E., and Cloetingh, S. (1992) Physical properties of the Europe's lithosphere. In Blundell,
D., Freeman, R., and Mueller, S. (Eds.) A continent revealed: The European Geotraverse:
Cambridge University Press, Cambridge, 71-80.
Bartov, Y., Steinitz, G., Eyal, M., and Eyal, Y. (1980) Sinistral movement along the Gulf of
Aqaba – its age and relation to the opening of the Red Sea. Nature, 285, 220-221.
Basseville, M., and Nikiforov, I.V. (1993) Detection of Abrupt Changes: Theory and
Application. Prentice Hall Information and System Science Series, Prentice Hall, Englewood
Cliffs, NJ.
Beardsmore, G.R., and Cull, J.P. (2001) Crustal Heat Flow: a guide to measurement and
modeling. Cambridge University Press, Cambridge.
Ben-Avraham, Z. (1997) Geophysical framework of the Dead Sea: structure and tectonics. In
Niemi, T.M., Ben-Avraham, Z., and Gat, J.R. (Eds.) The Dead Sea: The lake and its settings:
Oxford University Press, New York, NY, 36, 22-35.
Ben-Avraham, Z., and Von Herzen, R.P. (1987) Heat flow and continental breakup: the Gulf of
Elat (Aqaba). Journal of Geophysical Research, 92, 1407-1416.
Ben-Avraham, Z., Hänel, R., and Villinger, H. (1978) Heat flow through the Dead Sea rift.
Marine Geology, 28, 253-269.
Ben-Menahem, A. (1991) Four Thousand Years of Seismicity Along the Dead Sea Rift. Journal
of Geophysical Research, 96, B12, 20195-20216.
Berkhout, A.J., and Zaanen, P.R. (1976) A comparison between Wiener filtering, Kalman
filtering, and deterministic least squares estimation. Geophysical Prospecting, 24, 141-197.
Blackman, R.B., and Tukey, J.W. (1958) The Measurement of Power Spectra, Dover, New York,
NY.
Bode, H.W., and Shannon, C.E. (1950) A Simplified Derivation of Linear Least Square
Smoothing and Prediction Theory. Proceedings of the Institute of Radio Engineers, 38, 417425. Reprinted in Sloane, N.J.A., and Wyner, A.D. (Eds.) (1993) Claude Elwood Shannon
Collected Papers: IEEE Press, New York, NY, 628-636.
111
Brune, J.N. (1970) Tectonic Stress and the Spectra of Seismic Shear Waves from Earthquakes.
Journal of Geophysical Research, 75, 26, 4997-5009.
Bryant, A.S., and Jones, L.M. (1992) Anomalously Deep Crustal Earthquakes in the Ventura
Basin, Southern California. Journal of Geophysical Research, 97, 437-447.
Bullen, K.E. (1960) Note on Cusps in Seismic Travel-Times. Geophysical Journal of the Royal
Astronomical Society, 3, 354-359.
Burg, J.P. (1967) Maximum entropy spectral analysis. Paper presented at the 37th Annual
Meeting of the Society of Exploration Geophysicists, Oklahoma City, OK. Reprinted in
Childers, D.G. (Ed.) (1978) Modern spectrum analysis: IEEE Press, New York, NY, 34-41.
Burg, J.P. (1968) A new analysis technique for time series data. Paper presented at the NATO
Advanced Study Institute on Signal Processing with Emphasis on Underwater Acoustics,
Enschede, Netherlands. Reprinted in Childers, D.G. (Ed.) (1978) Modern spectrum analysis:
IEEE Press, New York, NY, 42-48.
Burg, J.P. (1975) Maximum entropy spectral analysis. Ph.D. thesis, Stanford University, pp. 123.
Byerlee, J.D. (1968) Brittle-ductile transition in rocks. Journal of Geophysical Research, 73,
4741-4750.
Byerlee, J.D. (1978) Friction of rocks. Pure and Applied Geophysics, 116, 615-626.
Camelbeek, T., and Iranga, M.D. (1996) Deep crustal earthquakes and geometry of active faults
along the Rukwa trough, East Africa. Geophysical Journal International, 124, 612–630.
Chen, W-P., and Molnar, P. (1983) Focal depths of intracontinental and intraplate earthquakes
and their implications for the thermal and mechanical properties of the lithosphere. Journal of
Geophysical Research, 88, B5, 4183-4214.
Childers, D.G. (Ed.) (1978) Modern spectrum analysis. IEEE Press, New York, NY.
Christensen, N.I., and Mooney, W.D. (1995) Seismic velocity structure and composition of the
continental crust: a global view. Journal of Geophysical Research, 100, B7, 9761-9788.
Cloetingh, S., and Ben-Avraham, Z. (Eds.) (2002) From continental extension to collision:
Africa-Europe interaction, the Dead Sea and analogue natural laboratories. EGU Stephan
Mueller Special Publication Series, 2.
Cloetingh, S., and Burov, E. (1996) Thermomechanical structure of European continental
lithosphere: constraints from rheological profiles and EET estimates. Geophysical Journal
International, 124, 695-723.
Creager, K.C. (1997) Coral. Seismological Research Letters, 68, 269-271.
Dai, H., and MacBeth, C. (1995) Automatic picking of seismic arrivals in local earthquake data
using an artificial neural network. Geophysical Journal International, 120, 758-774.Dai, H.,
and MacBeth, C. (1997) The application of back-propagation neural network to automatic
112
picking seismic arrivals from single-component recordings. Journal of Geophysical
Research, 102, 15105-15115.
Deichmann, N., and Rybach, L. (1989) Earthquakes and temperatures in the lower crust below
the northern alpine foreland of Switzerland. In Mereu, R.F., Mueller, S., Fountain, D.M.,
(Eds.) Properties and processes of the Earth’s Lower Crust: Geophysical Monograph 51,
IUGG, Vol. 6, American Geophysical Union, Washington, DC, 197-213.
Der, Z.A., and Shumway, R.H. (1999) Phase onset time estimation at regional distances using
the CUSUM algorithm. Physics of the Earth and Planetary Interiors, 113, 227-246.
Der, Z.A., McGarvey, M.W., and Shumway, R.H. (2000) Automatic interpretation of regional
short period seismic signals using the CUSUM-SA algorithm. Proceedings of the 22nd
DoD/DoE Seismic Research Symposium. New Orleans, LA.
DESERT Group, Weber, M., Abu-Ayyash, K., Abueladas, A., Agnon, A., Al-Amoush, H.,
Babeyko, A., Bartov, Y., Baumann, M., Ben-Avraham, Z., Bock, G., Bribach, J., El-Kelani,
R., Förster, A., Förster, H.-J., Frieslander, U., Garfunkel, Z., Grunewald, S., Götze, H.J.,
Haak, V., Haberland, C., Hassouneh, M., Helwig, S., Hofstetter, A., Jäckel, K.-H., Kesten,
D., Kind, R., Maercklin, N., Mechie, J., Mohsen, A., Neubauer, F.M., Oberhänsli, R.,
Qabbani, I., Ritter, O., Rümpker, G., Rybakov, M., Ryberg, T., Scherbaum, F., Schmidt, J.,
Schulze, A., Sobolev, S., Stiller, M., Thoss, H., Weckmann, U., and Wylegalla, K. (2004)
The crustal structure of the Dead Sea Transform. Geophysical Journal International, 156,
655-681.
Déverchère, J., Petit, C., Gileva, N., Radziminovitch, N., Melnikova, V., and San’kov, V. (2001)
Depth distribution of earthquakes in the Baikal rift system and its implications for the
rheology of the lithosphere. Geophysical Journal International, 146, 714-730.
Di Stefano, R., Aldersons, F., Kissling, E., Chiarabba, C., and Giardini, D. (2004) Automatic
seismic phase picking and consistent observation error assessment: Application to the Italian
seismicity. In preparation for submission to Geophysical Journal International.
Dodge, D.A., Beroza, G.C., and Ellsworth, W.L. (1995) Foreshock sequence of the 1992
Landers, California earthquake and its implications for earthquake nucleation. Journal of
Geophysical Research, 100, 9865-9880.
Douglas, A. (1997) Bandpass Filtering to Reduce Noise on Seismograms: Is There a Better
Way ? Bulletin of the Seismological Society of America, 87, 4, 770-777.
Douglas, A., Bowers, D., and Young, J.B. (1997) On the onset of P seismograms. Geophysical
Journal International, 129, 681-690.
Durbin, J. (1960) The fitting of time series models. Review of the International Institute of
Statistics, 28, 3, 233-244.
113
Eckstein, Y., and Simmons, G. (1978) Measurements and interpretation of terrestrial heat flow in
Israel. Geothermics, 6, 117-142.
El-Isa, Z.H. (1990) Lithospheric structure of the Jordan-Dead Sea transform from earthquake
data. Tectonophysics, 180, 29-36.
Erickson, A.J. (1970) The measurement and interpretation of heat flow in the Mediterranean and
Black Sea. Ph.D. thesis, Massachusetts Institute of Technology, pp. 433.
Fischer, R.A. (1936) The Use of Multiple Measurements in Taxonomic Problems. Annals of
Eugenics, 7, 179-188.
Fischer, R.A. (1938) The Statistical Utilization of Multiple Measurements. Annals of Eugenics,
8, 376-386.
Franklin, J.N. (1970) Well-posed stochastic extensions of ill-posed linear problems. Journal of
Mathematical Analysis and Applications, 31, 682-716.
Freund, R. (1965) A model of the structural development of Israel and adjacent areas since
Upper Cretaceous times. Geological Magazine, 102, 189-205.
Freund, R., Garfunkel, Z., Zak, I., Goldberg, M., Weissbrod, T., and Derin, B. (1970) The shear
along the Dead Sea rift. Philosophical Transactions of the Royal Society of London, Series
A, 267, 105-127.
Frieslander, U., and Ben-Avraham, Z. (1989) Magnetic field over the Dead Sea and vicinity.
Marine and Petroleum Geology, 6, 148-160.
Garfunkel, Z. (1997) The history and formation of the Dead Sea basin. In Niemi, T.M., BenAvraham, Z., and Gat, J.R. (Eds.) The Dead Sea: The lake and its settings: Oxford University
Press, New York, NY, 36, 36-52.
Garfunkel, Z. (1999) History and paleogeography during the Pan-African orogen to stable
platform transition: Reappraisal of the evidence from the Elat area and the northern ArabianNubian Shield. Israel Journal of Earth Sciences, 48, 135-157.
Gersch, W., and Sharpe, D.R. (1973) Estimation of power spectra with finite order
autoregressive models. IEEE Transactions on Automatic Control, AC-18, 367-369.
Ginzburg, A., and Ben-Avraham, Z. (1997) A seismic refraction study of the north basin of the
Dead Sea, Israel. Geophysical Research Letters, 24, 2063-2066.
Ginzburg, A., Makris, J., Fuchs, K., and Prodehl, C. (1981) The structure of the crust and upper
mantle in the Dead Sea rift. Tectonophysics, 80, 109-119.
Ginzburg, A., Makris, J., Fuchs, K., Perathoner, B., and Prodehl, C. (1979) Detailed Structure of
the Crust and Upper Mantle Along the Jordan-Dead Sea Rift. Journal of Geophysical
Research, 84, B10, 5605-5612.
Goetze, C. (1978) The mechanisms of creep in olivine. Philosophical Transactions of the Royal
Society of London, Series A, 288, 99-119.
114
Goldstein, P., Dodge, D., and Firpo, M. (1999) SAC2000: Signal processing and analysis tools
for seismologists and engineers, UCRL-JC-135963, Invited contribution to the IASPEI
International Handbook of Earthquake and Engineering Seismology.
GSE/JAPAN/40 (1992) A fully automated method for determining the arrival times of seismic
waves and its application to an on-line processing system. Paper tabled in the 34th GSE
session in Geneva GSE/RF/62.
Hansen, F.D., and Carter, N.L. (1982) Creep of selected crustal rocks at 1000 MPa. Eos
Transactions American Geophysical Union, 63, 437.
Haslinger, F. (1998) Velocity Structure, Seismicity and Seismotectonics of Northwestern Greece
Between the Gulf of Arta and Zakynthos. Ph.D. thesis, ETH, Zürich, pp. 160.
Havskov, J., and Ottemöller, L. (1999) SeisAn earthquake analysis software, Seismological
Research Letters, 70, 5, 532-534.
Hayes, M.H. (1996) Statistical digital signal processing and modeling. John Wiley, New York,
NY.
Jackson, J.A. (2002) Strength of the continental lithosphere: Time to abandon the jelly
sandwich ? GSA Today, 12, 9, 4-10.
Jaynes, E.T. (1957a) Information Theory and Statistical Mechanics. The Physical Review, 106,
4, 620-630.
Jaynes, E.T. (1957b) Information Theory and Statistical Mechanics. II. The Physical Review,
108, 2, 171-190.
Johnson, C.E., Lindh. A.G., and Hirshorn, B. (1994) Robust regional phase association. U.S.G.S.
Open File Report 94-621.
Johnson, S.J., and Anderson, N. (1978) On power estimation in maximum entropy spectrum
analysis. Geophysics, 43, 681-690.
Jones, R.H. (1974) Identification and Autoregressive Spectrum Estimation. IEEE Transactions
on Automatic Control, AC-19, 894-897. Reprinted in Childers, D.G. (Ed.) (1978) Modern
spectrum analysis: IEEE Press, New York, NY, 301-304.
Jones, R.H. (1976) Autoregression Order Selection. Geophysics, 41, 771-773. Reprinted in
Childers, D.G. (Ed.) (1978) Modern spectrum analysis: IEEE Press, New York, NY, 249251.
Jordan Seismological Observatory (JSO) (1993) Earthquakes in Jordan and Adjacent Areas, 25,
Amman, Jordan, 1-142.
Joswig, M., and Schulte-Theis, H. (1993) Master-event correlations of weak local earthquakes by
dynamic waveform matching. Geophysical Journal International, 113, 562-574.
Khintchine, A. (1934) Korrelationstheorie der stationären stochastischen Prozesse.
Mathematische Annalen, 109, 604-615.
115
Kirby, S.H. (1983) Rheology of the lithosphere. Reviews of Geophysics and Space Physics, 21,
6, 1458-1487.
Kameyama, M., Yuen, D.A., and Karato, S.-I. (1999) Thermal-mechanical effects of lowtemperature plasticity (the Peierls mechanism) on the deformation of a viscoelastic shear
zone. Earth and Planetary Science Letters, 168, 159-172.
Kissling, E. (1988) Geotomography with local earthquake data. Review of Geophysics, 26, 4,
659-698.
Kissling, E., Ellsworth, W.L., Eberhart-Phillips, D., and Kradolfer, U. (1994) Initial reference
models in local earthquake tomography. Journal of Geophysical Research, 99, 19635-19646.
Klumpen, E., and Joswig, M. (1993) Automated reevaluation of local earthquake data by
application of generic polarization patterns for P- and S-onsets. Computers & Geosciences,
19, 2, 223-231.
Kromer, R. (1970) Asymptotic properties of the autoregressive spectral estimator. Ph.D. thesis,
Stanford University.
Kushnir, A., Lapshin, V., Pinsky, V., and Fyen, J. (1990) Statistically optimal event detection
using small array data. Bulletin of the Seismological Society of America, 80, 6b, 1934-1950.
Lacoss, R.T. (1971) Data adaptive spectral analysis methods. Geophysics, 36, 661-675.
Reprinted in Childers, D.G. (Ed.) (1978) Modern spectrum analysis: IEEE Press, New York,
NY, 134-148.
Landers, T.E., and Lacoss, R.T. (1977) Some Geophysical Applications of Autoregressive
Spectral Estimates. IEEE Transactions on Geoscience Electronics, GE-15, 26-32. Reprinted
in Childers, D.G. (Ed.) (1978) Modern spectrum analysis. IEEE Press, New York, NY, 305311.
Langston, C.A. (1979) Structure under Mount Rainier, Washington, inferred from teleseismic
body waves. Journal of Geophysical Research, 84, 4749-4762.
Leonard, M. (2000) Comparison of Manual and Automatic Onset Time Picking. Bulletin of the
Seismological Society of America, 90, 6, 1384-1390.
Leonard, M., and Kennett, B.L.N. (1999) Multi-component autoregressive techniques for the
analysis of seismograms. Physics of the Earth and Planetary Interiors, 113, 247-263.
Levinson, N. (1947a) The Wiener RMS error criterion in filter design and prediction. Journal of
Mathematics and Physics, 25, 4, 261-278. Reprinted In Wiener, N. (1949) Extrapolation,
Interpolation, and Smoothing of Stationary Time Series with Engineering Applications: MIT
Press, Cambridge, MA, 129-148.
Levinson, N. (1947b) A heuristic exposition of Wiener’s mathematical theory of prediction and
filtering. Journal of Mathematics and Physics, 26, 2, 110-119. Reprinted In Wiener, N.
116
(1949) Extrapolation, Interpolation, and Smoothing of Stationary Time Series with
Engineering Applications: MIT Press, Cambridge, MA, 149-160.
Mackwell, S.J, Zimmerman, M.E., and Kohlstedt, D.L. (1998) High-temperature deformation of
dry diabase with applications to tectonics on Venus. Journal of Geophysical Research, 103,
B1, 975-984.
Maggi, A., Jackson, J.A., McKenzie, D., and Priestley, K. (2000) Earthquake focal depths,
effective elastic thickness, and the strength of the continental lithosphere. Geology, 28, 6,
495-498.
Marple, S.L.Jr. (1982) Frequency resolution of Fourier and maximum entropy spectral estimates.
Geophysics, 47, 9, 1303-1307.
McKenzie, D., and Fairhead, D. (1997) Estimates of the effective elastic thickness of the
continental lithosphere from Bouguer and free air gravity anomalies, Journal of Geophysical
Research, 102, 27523-27552.
Meissner, R., and Strehlau, L. (1982) Limits of stresses in continental crusts and their relation to
the depth-frequency distribution of shallow earthquakes. Tectonics, 1, 73-89.
Morita, Y., and Hamaguchi, H. (1984) Automatic detection of onset time of seismic waves and
its confidence interval using the autoregressive model fitting. Zisin, 37, 281-293.
Neev, D., and Hall, J. (1979) Geophysical investigations in the Dead Sea. Sedimentary Geology,
23, 209-238.
Nyblade, A.A., and Langston, C.A. (1995) East African earthquakes below 20 km and their
implications for crustal structure. Geophysical Journal International, 121, 49-62.
Oppenheim, A.V., Schafer, R.W., and Buck, J.R. (1999) Discrete-time signal processing, 2nd
edition. Prentice Hall, Upper Saddle River, N.J.
Park, J., Lindberg, C.R., and Vernon III, F.L. (1987) Multitaper Spectral Analysis of HighFrequency Seismograms. Journal of Geophysical Research, 92, B12, 12675-12684.
Pe’eri, S., Wdowinski, S., Shtibelman, A., Bechor, N., Bock, Y., Nikolaidis, R., and van
Domselaar, M. (2002) Current plate motion across the Dead Sea Fault from three years of
continuous GPS monitoring. Geophysical Research Letters, 10.1029/2001GL013879.
Penland, C., Ghil, M., and Weickmann, K.M. (1991) Adaptive Filtering and Maximum Entropy
Spectra With Application to Changes in Atmospheric Angular Momentum. Journal of
Geophysical Research, 96, D12, 22659-22671.
Peraldi, R., and Clement, A. (1972) Digital processing of refraction data study of first arrivals.
Geophysical Prospecting, 20, 529-548.
Percival, D.B., and Walden, A.T. (1993) Spectral Analysis for Physical Applications: multitaper
and conventional univariate techniques. Cambridge University press.
117
Piersanti, A., Nostro, C., and Riguzzi, F. (2001) Active displacement field in the Suez-Sinai area:
the role of postseismic deformation. Earth and Planetary Science Letters, 193, 13-23.
Press, W.H., Flannery, B.P., Teukolsky, S.A., and Vetterling, W.T. (1992) Numerical Recipes in
Fortran: The Art of Scientific Computing, 2nd edition. Cambridge University Press,
Cambridge, England.
Prodehl, C., Fuchs, K., and Mechie, J. (1997) Seismic-refraction studies of the Afro-Arabian rift
system – a brief review. Tectonophysics, 278, 1-13.
Quennell, A.M. (1958) The structural and geomorphic evolution of the Dead Sea rift. Quarterly
Journal of the Geological Society of London, 114, 1-24.
Rabiner, L.R., and Schafer, R.W. (1978) Digital Processing of Speech Signals. Prentice-Hall,
Englewood Cliffs, NJ.
Rabinowitz, N., Steinberg, J., and Mart, Y. (1996) New evidence of magmatic diapirs in the
intermediate crust under the Dead Sea, Israel. Tectonics, 15, 2, 237-243.
Rabinowitz, N., and Mart, Y. (2000) Seismic tomography of the Dead Sea region: thinned crust,
anomalous velocities and possible magmatic diapirism. In Vendeville, B., Mart, Y., and
Vigneresse, J.-L.: Salt, shale, and Igneous Diapirs in and around Europe, Geological Society,
Special Publications, London, 174, 79-92.
Ranalli, G. (1987) Rheology of the Earth: Deformation and flow processes in geophysics and
geodynamics. Allen and Unwin, Boston, MA.
Ranalli, G., and Murphy, D.C. (1987) Rheological stratification of the lithosphere.
Tectonophysics, 132, 281-295.
Rodgers, J.J.W., and Adams, J.A.S. (1969) Uranium and Thorium. In Wedepohl, K.H. (Ed.)
Handbook of Geochemistry, Vol. II/1: Springer, Berlin, 92K1-92K8 and 90K1-90K3.
Rowe, C.A., Aster, R.C., Borchers, B., and Young, C.J. (2002) An Automatic, Adaptive
Algorithm for Refining Phase Picks in Large Seismic Data Sets. Bulletin of the
Seismological Society of America, 92, 5, 1660-1674.
Roy, M., and Royden, L.H. (2000a) Crustal rheology and faulting at strike-slip plate boundaries
1. An analytic model. Journal of Geophysical Research, 105, B3, 5583-5597.
Roy, M., and Royden, L.H. (2000b) Crustal rheology and faulting at strike-slip plate boundaries
2. Effects of lower crustal flow. Journal of Geophysical Research, 105, B3, 5599-5613.
Rybach, L., and Buntebarth, G. (1984) The variation of heat generation, density and seismic
velocity with rock type in the continental lithosphere. Tectonophysics, 103, 335-344.
Scherbaum, F. (1996) Of Poles and Zeros: Fundamentals of Digital Seismometry. Kluwer
Academic Publishers, Dordrecht, The Netherlands.
118
Scherbaum, F. and Johnson, J. (1992) Programmable Interactive Toolbox for Seismological
Analysis (PITSA). IASPEI Software Library Volume 5, Seismological Society of America,
El Cerrito.
Scholz, C.H. (2002) The Mechanics of Earthquakes and Faulting, 2nd edition. Cambridge
University Press, Cambridge, England.
Shannon, C.E. (1948) A Mathematical Theory of Communication. The Bell System Technical
Journal, 27, 379-423 (July) and 623-656 (October). Reprinted in Sloane, N.J.A., and Wyner,
A.D. (Eds.) (1993) Claude Elwood Shannon: collected papers: IEEE Press, New York, NY,
5-83.
Shapira, A. (1997) On the seismicity of the Dead Sea basin. In Niemi, T.M., Ben -Avraham, Z.,
and Gat, J.R. (Eds.) The Dead Sea: The lake and its settings: Oxford University Press, New
York, NY, 36, 82-86.
Shapira, A., Avni, R., and Nur, A. (1993) A note: New estimate of the Jericho earthquake
epicenter of July 11, 1927. Israel Journal of Earth Sciences, 42, 93-96.
Shearer, P.M. (1997) Improving local earthquake locations using the L1 norm and waveform
cross correlation: Application to the Whittier Narrows, California, aftershock sequence.
Journal of Geophysical Research, 102, 8269-8283.
Shelton, G., and Tullis, J.A. (1981) Experimental flow laws for crustal rocks (abstract). Eos
Transactions American Geophysical Union, 62, 396.
Shudofsky, G., Cloetingh, S., Stein, S., and Wortel, R. (1987) Unusually deep earthquakes in
East Africa: Constraints on the thermo-mechanical structure of a continental rift system.
Geophysical Research Letters, 14, 741-744.
Schuster, A. (1898) On the investigation of hidden periodicities with application to a supposed
twenty-six day period of meteorological phenomena. Terrestrial Magnetism, 3, 1, 13-41.
Sibson, R.H. (1974) Frictional constraints on thrust, wrench and normal faults. Nature, 249, 542544.
Sleeman, R., and van Eck, T. (1999) Robust automatic P-phase picking: an on-line
implementation in the analysis of broadband seismogram recordings. Physics of the Earth
and Planetary Interiors, 113, 265-275.
Smylie, D.E., Clarke, G.K.C., and Ulrych, T.J. (1973) Analysis of irregularities in the earth's
rotation. In Bolt, B.A. (Ed.) Methods in computational physics, vol. 13: Academic Press,
New York, NY, 391-430.
Stiller, M., Yanaki, N.E., and Kronfeld, J. (1985) Comparative isotope study of two short
sediment cores from the Dead Sea. Chemical Geology (Isotope Geoscience Section), 58,
107-119.
119
Takanami, T., and Kitagawa, G. (1988) A new efficient procedure for the estimation of onset
times of seismic waves. Journal of Physics of the Earth, 36, 267-290.
Takanami, T., and Kitagawa, G. (Eds.) (2003) Methods and Applications of Signal Processing in
Seismic Network Operations. Springer, Berlin, Lecture Notes in Earth Sciences, 98.
ten Brink, U.S. (2002) Corrigendum to ‘Lower crustal flow and the role of shear in basin
subsidence: an example from the Dea Sea basin’. Earth and Planetary Science Letters, 201,
447-448.
ten Brink, U.S., and Ben-Avraham, Z. (1989) The anatomy of a pull-apart basin: seismic
reflection observations of the Dead Sea basin. Tectonics, 2, 333-350.
ten Brink, U.S., Kovach, R.L., Schoenberg, N., and Ben-Avraham, Z. (1990) Uplift and a
possible Moho offset across the Dead Sea transform. Tectonophysics, 180, 71-85.
ten Brink, U.S., Ben-Avraham, Z., Bell, R., Hassouneh, M., Coleman, D., Andreasen, G., Tibor,
G., and Coakley, B. (1993) Structure of the Dead Sea pull-apart basin from gravity analysis.
Journal of Geophysical Research, 98, 21877-21894.
Thomson, J.D. (1982) Spectrum estimation and harmonic analysis. Proceedings of the Institute
of Electrical and Electronics Engineers (IEEE), 70, 1055-1096.
Thurber, C.H. (1984) SIMUL3. In Engdahl, E.R. (Ed.) Documentation of Earthquake
Algorithms: Report SE-35, World Data Center A for Solid Earth Geophysics, Boulder,
Colorado, 15-17.
Turcotte, D.L., and Schubert, G. (2002) Geodynamics, 2nd edition. Cambridge University Press,
Cambridge, England.
Turcotte, T., and Arieh, E. (1988) Catalog of earthquakes in and around Israel. In Preliminary
safety analysis report: Israel Electric Corporation, Tel Aviv, 1-18.
Ulrych, T.J., and Bishop, T.N. (1975) Maximum Entropy Spectral Analysis and Autoregressive
Decomposition. Revue of Geophysics and Space Physics, 13, 183-200. Reprinted in
Childers, D.G. (Ed.) (1978) Modern spectrum analysis: IEEE Press, New York, NY, 54-71.
van den Bos, A. (1971) Alternative Interpretation of Maximum Entropy Spectral Analysis. IEEE
Transactions on Information Theory, IT-17, 493-494. Reprinted in Childers, D.G. (Ed.)
(1978) Modern spectrum analysis: IEEE Press, New York, NY, 92-93.
van Eck, T., and Hofstetter, A. (1989) Microearthquake activity in the Dead Sea region.
Geophysical Journal International, 99, 605-620.
van Eck, T., and Hofstetter, A. (1990) Fault geometry and spatial clustering of microearthquakes
along the Dead Sea-Jordan rift fault zone. Tectonophysics, 180, 15-27.
Vaseghi, S. (2000) Advanced Digital Signal Processing and Noise Reduction, 2nd edition. John
Wiley, Chichester, West Sussex, England.
Walker, G. (1931) On periodicity in series of related terms. Proceedings of the Royal Society of
120
London, Series A, 131, 518-532.
Wiener, N. (1930) Generalized harmonic analysis. Acta Mathematica, 55, 117-258.
Wiener, N. (1949) Extrapolation, Interpolation, and Smoothing of Stationary Time Series with
Engineering Applications. MIT Press, Cambridge, MA.
Wong, I., and Chapman, D. (1990) Deep intraplate earthquakes in the western United States and
their relationship to lithospheric temperatures. Bulletin of the Seismological Society of
America, 80, 589-599.
Wu, N. (1997) The maximum entropy method. Springer, Berlin.
Yule, G.U. (1927) On a method of investigating periodicities in disturbed series, with special
reference to Wolfer's sunspot numbers. Philosophical Transactions of the Royal Society of
London, Series A, 226, 267-298.
121
Acknowledgments
I want to particularly thank my two advisors Prof. Zvi Ben-Avraham from Tel Aviv University
and Prof. Edi Kissling from ETH Zürich. I knew from the start that I would be in good hands
working with them, and I can truly say that this feeling only grew over the years. As I moved my
non-portable computer to three continents before concluding the work, I am also very grateful to
them for their trust. Since most of my time was spent working from home, I really enjoyed and I
miss now our Monday afternoon sessions “on the roof” at TAU where every week members of
the Minerva Dead Sea Research Center share the progress of their work with the others. I want to
thank Michael Lazar for his translations to or from Hebrew and for having paid my tuition fees
when I was living far from the Middle East. Thanks a lot also to Uri Schattner for his meticulous
translation to Hebrew of the cover page and abstract of the thesis.
I particularly thank also the Ministry of Energy and Infrastructure of Israel and Dr. Yossi Bartov
for the financial support of this work during two years.
I got plenty of seismological data from the Geophysical Institute of Israel, and I thank Dr. Avi
Shapira for this opportunity. I particularly thank Dr. Abraham Hofstetter for his interest,
involvement and help in this work. I thank also Dr. Nitzan Rabinowitz for having kindly allowed
me to attend the Shalheveth Freier First International Workshop on Advanced Methods in
Seismic Analysis, held at the Dead Sea in January 1998. Alona Malitzky introduced me to the
binary format of seismograms at GII. I greatly thank Lea Feldman and Batia Reich for their help
to retrieve, and for retrieving so many of the seismograms. Corinne Ben-Sasson helped to solve
many practical issues.
I got also plenty of data from the Jordanian Seismological Observatory for which I am very
thankful to Dr. Abdel-Qader Amrat. I particularly thank Dr. Tawfiq Al-Yazjeen for his interest,
commitment and help along the road of the project. The few trips I did to NRA in Amman were
always fruitful thanks to him. What a surprise also to meet Bassam Al-Biss again, after we
briefly worked together in 1988 in the oil exploration of the Djebel Druze region in Jordan.
Discussions with Dr. Manfred Baer were very useful to better understand how his picking
algorithm works and I thank him also for providing his valuable code as a freeware contribution
to the seismological community. I thank Dr. E.R. Engdahl, Dr. W.L. Ellsworth and Dr. W.
Kohler for having provided me with the source code of the R. Allen picking system.
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Raffaele di Stefano endured with good will a lot of beta testing of MannekenPix before version
1.6.2 allowed him to work in production mode on his data sets of Italy. Thanks for your patience
Raffaele.
Most of the library work for the lower-crustal study of the Dead Sea was done at LamontDoherty. I thank Dr. Michael Steckler for granting me access to the library and Mary Ann
Brueckner for her very kind help on the spot.
I thank also André Van Moer who introduced me to Matlab and to the Watcom compilers 10
years ago in central Africa. I still use them today. Frances and Russ improved the Lower-crustal
manuscript. Our nanny Jessica and “Nonna” Iris did a pretty number of extra hours to take care
of the kids.
But of course Marilena’s support was essential. Without my spouse’s natural resistance from
earthquake-prone Friuli and financial support when no funding was available, this work could
never have been completed. For Elisa and Francesco, the most important thing is probably that
dad is back home now.
I finally thank Prof. Sierd Cloetingh, Prof. George Poupinet, and an anonymous reviewer for
having accepted to review the thesis and for their constructive criticism.
Thanks to all of you.
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